Updated on 2024/02/15

写真b

 
KOMORI Yasushi
 
*Items subject to periodic update by Rikkyo University (The rest are reprinted from information registered on researchmap.)
Affiliation*
College of Science Department of Mathematics
Graduate School of Science Doctoral Program in Mathematics
Graduate School of Science Master's Program in Mathematics
Title*
Professor
Degree
博士(理学) ( 東京大学 )
Research Theme*
  • 研究テーマは可積分系、および関連する数理である。具体的には、物理に現れる微分方程式や差分方程式、特殊関数について、リー群やリー代数、ワイル群などの代数構造とその表現論を用いて解析している。最近は量子ゲージ理論や解析数論などに現れる多重ゼータ関数について研究を進めている。

  • Campus Career*
    • 4 2017 - Present 
      College of Science   Department of Mathematics   Professor
    • 4 2017 - Present 
      Graduate School of Science   Master's Program in Mathematics   Professor
    • 4 2017 - Present 
      Graduate School of Science   Doctoral Program in Mathematics   Professor
    • 4 2010 - 3 2017 
      College of Science   Department of Mathematics   Associate Professor
    • 4 2010 - 3 2017 
      Graduate School of Science   Master's Program in Mathematics   Associate Professor
    • 4 2010 - 3 2017 
      Graduate School of Science   Doctoral Program in Mathematics   Associate Professor

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    Research Areas

    • Natural Science / Mathematical physics and fundamental theory of condensed matter physics

    • Natural Science / Algebra

    Research History

    • 4 2017 - Present 
      RIKKYO UNIVERSITY   College of Science Department of Mathematics   Professor

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    • 4 2017 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Professor

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    • 4 2017 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Professor

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    • 4 2010 - 3 2017 
      RIKKYO UNIVERSITY   College of Science Department of Mathematics   Associate Professor

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    • 4 2007 - 3 2010 
      Nagoya University   Graduate School of Mathematics

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    • 9 2001 - 3 2007 
      Nagoya University   Graduate School of Mathematics

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    • 4 2000 - 8 2001 
      東京大学大学院総合文化研究科   日本学術振興会特別研究員

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    • 4 2000 - 8 2001 
      The University of Tokyo   Graduate School of Arts and Sciences

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    • 4 1997 - 3 2000 
      東京大学大学院理学系研究科物理学専攻   日本学術振興会特別研究員

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    • 4 1997 - 3 2000 
      The University of Tokyo   Graduate School of Science, Department of Physics

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    Education

    • - 3 2000 
      The University of Tokyo   Graduate School, Division of Science

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      Country: Japan

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    • - 3 1997 
      The University of Tokyo   Graduate School, Division of Science

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      Country: Japan

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    • - 3 1995 
      The University of Tokyo   Faculty of Science

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      Country: Japan

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    Papers

    • Finite multiple zeta values, symmetric multiple zeta values and unified multiple zeta functions Peer-reviewed

      Yasushi Komori

      Tohoku Mathematical Journal73 ( 2 )   1 6 2021

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      Publishing type:Research paper (scientific journal)   Publisher:Mathematical Institute, Tohoku University  

      DOI: 10.2748/tmj.20200226

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    • A CONGRUENCE BETWEEN SYMMETRIC MULTIPLE ZETA-STAR VALUES AND MULTIPLE ZETA-STAR VALUES Peer-reviewed

      Kento FUJITA, Yasushi KOMORI

      Kyushu Journal of Mathematics75 ( 1 ) 149 - 167   2021

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      Publishing type:Research paper (scientific journal)   Publisher:Faculty of Mathematics, Kyushu University  

      DOI: 10.2206/kyushujm.75.149

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    • Zeta-functions of root systems and Poincaré polynomials of Weyl groups Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      Tohoku Mathematical Journal72 ( 1 ) 87 - 126   3 2020

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Mathematical Institute, Tohoku University  

      We consider a certain linear combination $S(\mathbf{s},\mathbf{y};I;\Delta)$
      of zeta-functions of root systems, where $\Delta$ is a root system of rank $r$
      and $I\subset\{1,2,\ldots,r\}$. Showing two different expressions of
      $S(\mathbf{s},\mathbf{y};I;\Delta)$, we find that a certain signed sum of
      zeta-functions of root systems is equal to a sum involving Bernoulli functions
      of root systems. This identity gives a non-trivial functional relation among
      zeta-functions of root systems, if the signed sum does not identically vanish.
      This is a genralization of the authors' previous result proved in
      \cite{KMTLondon}, in the case when $I=\emptyset$. We present several explicit
      examples of such functional relations. A criterion of the non-vanishing of the
      signed sum, in terms of Poincar{\'e} polynomials of associated Weyl groups, is
      given. Moreover we prove a certain converse theorem, which implies that the
      generating function for the case $I=\emptyset$ essentially knows all
      information on generating functions for general $I$.

      DOI: 10.2748/tmj/1585101623

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    • An overview and supplements to the theory of functional relations for zeta functions of root systems Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      Advanced Studies in Pure Mathematics84   263 - 295   2020

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      Language:English  

      We give an overview of the theory of functional relations for zeta-functions
      of root systems, and show some new results on functional relations involving
      zeta-functions of root systems of types $B_r$, $D_r$, $A_3$ and $C_2$. To show
      those new results, we use two different methods. The first method, for $B_r$,
      $D_r$, $A_3$, is via generating functions, which is based on the symmetry with
      respect to Weyl groups, or more generally, on our theory of lattice sums of
      certain hyperplane arrangements. The second method for $C_2$ is more
      elementary, using partial fraction decompositions.

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    • FINITE MULTIPLE ZETA VALUES, MULTIPLE ZETA FUNCTIONS AND MULTIPLE BERNOULLI POLYNOMIALS Peer-reviewed

      Yasushi Komori

      KYUSHU JOURNAL OF MATHEMATICS72 ( 2 ) 333 - 342   8 2018

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:KYUSHU UNIV, FAC MATHEMATICS  

      We present explicit formulas for all finite multiple zeta values by introducing a multiple generalization of Bernoulli polynomials associated with finite multiple zeta values. Furthermore we show that these values are also described by special values of multiple zeta functions and multiple star analogues of the Hurwitz zeta function.

      DOI: 10.2206/kyushujm.72.333

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    • On Arakawa–Kaneko zeta-functions associated with $GL_2(\mathbb{C})$ and their functional relations Peer-reviewed

      Yasushi KOMORI, Hirofumi TSUMURA

      Journal of the Mathematical Society of Japan70 ( 1 ) 179 - 213   1 2018

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      Publishing type:Research paper (scientific journal)   Publisher:Mathematical Society of Japan (Project Euclid)  

      DOI: 10.2969/jmsj/07017501

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    • Desingularization of multiple zeta functions of generalized Hurwitz-Lerch type Peer-reviewed

      H. Furusho, Y. Komori, K. Matsumoto, H. Tsumura

      RIMS Kokyuroku BessatsuB68   27 - 66   2017

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    • Desingularization of complex multiple zeta-functions Peer-reviewed

      Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      American Journal of Mathematics139 ( 1 ) 147 - 173   2017

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      Publishing type:Research paper (scientific journal)   Publisher:Project Muse  

      DOI: 10.1353/ajm.2017.0002

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    • Fundamentals of p-adic multiple L-functions and evaluation of their special values Peer-reviewed

      Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      Selecta Mathematica23 ( 1 ) 39 - 100   1 2017

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      Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

      DOI: 10.1007/s00029-016-0233-2

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      Other Link: http://link.springer.com/article/10.1007/s00029-016-0233-2/fulltext.html

    • Duality Transformation Formulas for Multiple Elliptic Hypergeometric Series of Type $BC$ Peer-reviewed

      Yasushi Komori, Yasuho Masuda, Masatoshi Noumi

      Constructive Approximation44 ( 3 ) 483 - 516   12 2016

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

      New duality transformation formulas are proposed for multiple elliptic
      hypergeometric series of type $BC$ and of type $C$. Various transformation and
      summation formulas are derived as special cases to recover some previously
      known results.

      DOI: 10.1007/s00365-015-9316-0

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      Other Link: http://link.springer.com/article/10.1007/s00365-015-9316-0/fulltext.html

    • On the zeros of Weng zeta functions for Chevalley groups Peer-reviewed

      Haseo Ki, Yasushi Komori, Masatoshi Suzuki

      MANUSCRIPTA MATHEMATICA148 ( 1-2 ) 119 - 176   9 2015

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER HEIDELBERG  

      We prove that all but finitely many zeros of Weng's zeta function for a Chevalley group defined over Q are simple and on the critical line.

      DOI: 10.1007/s00229-015-0736-8

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    • Zeta-functions of weight lattices of compact semisimple connected Lie groups Peer-reviewed

      Y. Komori, K. Matsumoto, H. Tsumura

      Šiauliai Mathematical Seminar10   149 - 179   2015

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      We define zeta-functions of weight lattices of compact connected semisimple
      Lie groups. If the group is simply-connected, these zeta-functions coincide
      with ordinary zeta-functions of root systems of associated Lie algebras. In
      this paper we consider the general connected (but not necessarily
      simply-connected) case, prove the explicit form of Witten's volume formulas for
      these zeta-functions, and further prove functional relations among them which
      include their volume formulas.

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    • ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS V Peer-reviewed

      YASUSHI KOMORI, KOHJI MATSUMOTO, HIROFUMI TSUMURA

      Glasgow Mathematical Journal57 ( 1 ) 107 - 130   1 2015

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Cambridge University Press (CUP)  

      <title>Abstract</title>We study the values of the zeta-function of the root system of type <italic>G</italic><sub>2</sub> at positive integer points. In our previous work we considered the case when all integers are even, but in the present paper we prove several theorems which include the situation when some of the integers are odd. The underlying reason why we may treat such cases, including odd integers, is also discussed.

      DOI: 10.1017/s0017089514000160

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    • A study on multiple zeta values from the viewpoint of zeta-functions of root systems Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      Functiones et Approximatio Commentarii Mathematici51 ( 1 ) 43 - 76   9 2014

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      Publishing type:Research paper (scientific journal)   Publisher:Adam Mickiewicz University (Euclid)  

      We study multiple zeta values (MZVs) from the viewpoint of zeta-functions
      associated with the root systems which we have studied in our previous papers.
      In fact, the $r$-ple zeta-functions of Euler-Zagier type can be regarded as the
      zeta-function associated with a certain sub-root system of type $C_r$. Hence,
      by the action of the Weyl group, we can find new aspects of MZVs which imply
      that the well-known formula for MZVs given by Hoffman and Zagier coincides with
      Witten's volume formula associated with the above sub-root system of type
      $C_r$. Also, from this observation, we can prove some new formulas which
      especially include the parity results of double and triple zeta values. As
      another important application, we give certain refinement of restricted sum
      formulas, which gives restricted sum formulas among MZVs of an arbitrary depth
      $r$ which were previously known only in the cases of depth $2,3,4$.
      Furthermore, considering a sub-root system of type $B_r$ analogously, we can
      give relevant analogues of the Hoffman-Zagier formula, parity results and
      restricted sum formulas.

      DOI: 10.7169/facm/2014.51.1.3

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    • Infinite series involving hyperbolic functions Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      LITHUANIAN MATHEMATICAL JOURNAL55 ( 1 ) 102 - 118   31 8 2014

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      Language:English   Publisher:SPRINGER  

      In the former part of this paper, we summarize our previous results on
      infinite series involving the hyperbolic sine function, especially, with a
      focus on the hyperbolic sine analogue of Eisenstein series. Those are based on
      the classical results given by Cauchy, Mellin and Kronecker. In the latter
      part, we give new formulas for some infinite series involving the hyperbolic
      cosine function.

      DOI: 10.1007/s10986-015-9268-x

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    • Lattice sums of hyperplane arrangements Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi63 ( 1 ) 161 - 213   8 8 2014

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      Language:English  

      We introduce certain lattice sums associated with hyperplane arrangements,
      which are (multiple) sums running over integers, and can be regarded as
      generalizations of certain linear combinations of zeta-functions of root
      systems. We also introduce generating functions of special values of those
      lattice sums, and study their properties by virtue of the theory of convex
      polytopes. Consequently we evaluate special values of those lattice sums,
      especially certain special values of zeta-functions of root systems and their
      affine analogues. In some special cases it is possible to treat sums running
      over positive integers, which may be regarded as zeta-functions associated with
      hyperplane arrangements.

      DOI: 10.14992/00010883

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    • Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and q-zeta functions Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      FORUM MATHEMATICUM26 ( 4 ) 1071 - 1115   7 2014

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:WALTER DE GRUYTER GMBH  

      We consider certain double series of Eisenstein type involving hyperbolic-sine functions. We define certain generalized Hurwitz numbers, in terms of which we evaluate those double series. Our main results can be regarded as a certain generalization of well-known results of Hurwitz, Herglotz, Katayama and so on. Our results also include recent formulas of the third-named author which are double analogues of the formulas of Cauchy, Mellin, Ramanujan, Berndt and so on, about certain Dirichlet series involving hyperbolic functions. As an application, we give some evaluation formulas for q-zeta functions at positive integers.

      DOI: 10.1515/forum-2011-0300

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    • Spherical functions on the space of $p$-adic unitary hermitian matrices II, the case of odd size Peer-reviewed

      Yumiko Hironaka, Yasushi Komori

          15 3 2014

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      We are interested in the harmonic analysis on $p$-adic homogeneous spaces
      based on spherical functions. In the present paper, we investigate the space
      $X$ of unitary hermitian matrices of odd size over a ${\mathfrak p}$-adic field
      of odd residual characteristic, which is a continuation of our previous paper
      where we have studied for even size matrices. First we give the explicit
      representatives of the Cartan decomposition of $X$ and introduce a typical
      spherical function $\omega(x;z)$ on $X$. After studying the functional
      equations, we give an explicit formula for $\omega(x;z)$, where Hall-Littlewood
      polynomials of type $C_n$ appear as a main term, though the unitary group
      acting on $X$ is of type $BC_n$. By spherical transform, we show the Schwartz
      space ${\mathcal S}(K \backslash X)$ is a free Hecke algebra ${\mathcal H}(G,
      K)$-module of rank $2^n$, where $2n+1$ is the size of matrices in $X$, and give
      parametrization of all the spherical functions on $X$ and the explicit
      Plancherel formula on ${\mathcal S}(K \backslash X)$.

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    • Functional equations of Weng's zeta functions for $(G,P)/\mathbb{Q}$ Peer-reviewed

      Yasushi Komori

      American Journal of Mathematics135 ( 4 ) 1019 - 1038   2013

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Project Muse  

      It is shown that Weng's zeta functions associated with arbitrary semisimple
      algebraic groups defined over the rational number field and their maximal
      parabolic subgroups satisfy the functional equations.

      DOI: 10.1353/ajm.2013.0032

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    • Barnes multiple zeta-functions, Ramanujan's formula, and relevant series involving hyperbolic functions Peer-reviewed

      Y. Komori, K. Matsumoto, H. Tsumura

      Journal of the Ramanujan Mathematical Society28 ( 1 ) 49 - 69   2013

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      Language:English   Publisher:RAMANUJAN MATHEMATICAL SOC  

      In the former part of this paper, we give functional equations for Barnes
      multiple zeta-functions and consider some relevant results. In particular, we
      show that Ramanujan's classical formula for the Riemann zeta values can be
      derived from functional equations for Barnes zeta-functions. In the latter half
      part, we generalize some evaluation formulas of certain series involving
      hyperbolic functions in terms of Bernoulli polynomials. The original formulas
      were classically given by Cauchy, Mellin, Ramanujan, and later recovered and
      formulated by Berndt. From our consideration, we give multiple versions of
      these known formulas.

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    • Spherical functions on the space of $p$-adic unitary hermitian matrices Peer-reviewed

      Yumiko Hironaka, Yasushi Komori

      INTERNATIONAL JOURNAL OF NUMBER THEORY10 ( 2 )   26 7 2012

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      Language:English   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

      We investigate the space $X$ of unitary hermitian matrices over $\frp$-adic
      fields through spherical functions. First we consider Cartan decomposition of
      $X$, and give precise representatives for fields with odd residual
      characteristic, i.e., $2\notin \frp$. In the latter half we assume odd residual
      characteristic, and give explicit formulas of typical spherical functions on
      $X$, where Hall-Littlewood symmetric polynomials of type $C_n$ appear as a main
      term, parametrization of all the spherical functions. By spherical Fourier
      transform, we show the Schwartz space $\SKX$ is a free Hecke algebra
      $\hec$-module of rank $2^n$, where $2n$ is the size of matrices in $X$, and
      give the explicit Plancherel formula on $\SKX$.

      DOI: 10.1142/S1793042113501066

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    • Functional relations for zeta-functions of weight lattices of Lie groups of type $A_3$ Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      ANALYTIC AND PROBABILISTIC METHODS IN NUMBER THEORY   151 - +   4 2 2012

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      Language:English   Publisher:TEV LTD  

      We study zeta-functions of weight lattices of compact connected semisimple
      Lie groups of type $A_3$. Actually we consider zeta-functions of SU(4), SO(6)
      and PU(4), and give some functional relations and new classes of evaluation
      formulas for them.

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    • On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      Multiple Dirichlet Series, L-functions and Automorphic Forms62 ( 2 ) 223 - 286   2012

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      Language:English   Publishing type:Part of collection (book)   Publisher:Birkhäuser Boston  

      We prove certain general forms of functional relations among Witten multiple
      zeta-functions in several variables (or zeta-functions of root systems). The
      structural background of those functional relations is given by the symmetry
      with respect to Weyl groups. From those relations we can deduce explicit
      expressions of values of Witten zeta-functions at positive even integers, which
      is written in terms of generalized Bernoulli numbers of root systems.
      Furthermore we introduce generating functions of those Bernoulli numbers of
      root systems, by which we can give an algorithm of calculating Bernoulli
      numbers of root systems.

      DOI: 10.1007/978-0-8176-8334-4_11

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    • FUNCTIONAL EQUATIONS FOR DOUBLE L-FUNCTIONS AND VALUES AT NON-POSITIVE INTEGERS Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      INTERNATIONAL JOURNAL OF NUMBER THEORY7 ( 6 ) 1441 - 1461   9 2011

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

      We consider double L-functions with periodic coefficients and complex parameters. We prove functional equations for them, which is of traditional symmetric form on certain hyperplanes. These are character analogs of our previous result on double zeta-functions. We further evaluate double L-functions at non-positive integers and construct certain p-adic double L-functions.

      DOI: 10.1142/S1793042111004551

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    • Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      Mathematische Zeitschrift268 ( 3-4 ) 993 - 1011   8 2011

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

      The shuffle product plays an important role in the study of multiple zeta
      values. This is expressed in terms of multiple integrals, and also as a product
      in a certain non-commutative polynomial algebra over the rationals in two
      indeterminates. In this paper, we give a new interpretation of the shuffle
      product. In fact, we prove that the procedure of shuffle products essentially
      coincides with that of partial fraction decompositions of multiple zeta values
      of root systems. As an application, we give a proof of extended double shuffle
      relations without using Drinfel'd integral expressions for multiple zeta
      values. Furthermore, our argument enables us to give some functional relations
      which include double shuffle relations.

      DOI: 10.1007/s00209-010-0705-6

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      Other Link: http://link.springer.com/article/10.1007/s00209-010-0705-6/fulltext.html

    • Multiple zeta values and zeta-functions of root systems Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES87 ( 6 ) 103 - 107   6 2011

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:JAPAN ACAD  

      We propose the viewpoint that the r-ple zeta-function of Euler-Zagier type can be regarded as a specialization of the zeta-function associated with the root system of C-r type. From this viewpoint, we can see that Zagier's well-known formula for multiple zeta values (MZVs) coincides with Witten's volume formula associated with a sub-root system of C-r type. Based on this observation, we generalize Zagier's formula and also give analogous results which correspond to a sub-root system of B-r type. We announce those results as well as some relevant results for partial multiple zeta values.

      DOI: 10.3792/pjaa.87.103

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    • Evaluation formulas of Cauchy-Mellin type for certain series involving hyperbolic functions Peer-reviewed

      Y. Komori, K. Matsumoto, H. Tsumura

      Commentarii mathematici Universitatis Sancti Pauli60 ( 1 ) 127 - 142   2011

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      Language:English   Publisher:Rikkyo University  

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    • A survey on the theory of multiple Bernoulli polynomials and multiple L-functions of root systems Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      INFINITE ANALYSIS 2010: DEVELOPMENTS IN QUANTUM INTEGRABLE SYSTEMSB28   99 - 120   2011

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      Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:RESEARCH INST MATHEMATICAL SCIENCES, KYOTO UNIV  

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    • ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV Peer-reviewed

      YASUSHI KOMORI, KOHJI MATSUMOTO, HIROFUMI TSUMURA

      Glasgow Mathematical Journal53 ( 1 ) 185 - 206   1 2011

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Cambridge University Press (CUP)  

      <title>Abstract</title>In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types <italic>A</italic><sub>2</sub>, <italic>A</italic><sub>3</sub>, <italic>B</italic><sub>2</sub>, <italic>B</italic><sub>3</sub> and <italic>C</italic><sub>3</sub>. In this paper, we consider the case of <italic>G</italic><sub>2</sub>-type. We define certain analogues of Bernoulli polynomials of <italic>G</italic><sub>2</sub>-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of <italic>G</italic><sub>2</sub>-type. Next, we consider the meromorphic continuation of the zeta-function of <italic>G</italic><sub>2</sub>-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.

      DOI: 10.1017/s0017089510000613

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    • AN INTEGRAL REPRESENTATION OF MULTIPLE HURWITZ-LERCH ZETA FUNCTIONS AND GENERALIZED MULTIPLE BERNOULLI NUMBERS Peer-reviewed

      Yasushi Komori

      QUARTERLY JOURNAL OF MATHEMATICS61 ( 4 ) 437 - 496   12 2010

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:OXFORD UNIV PRESS  

      A surface integral representation of a multiple generalization of the Hurwitz-Lerch zeta function is given, which is a direct analogue of the well-known contour integral representation of the Riemann zeta function of Hankel's type. From this integral representation, we derive a detailed description of the set of its possible singularities. In addition, we present two formulae for special values of the zeta function at non-positive integers in terms of generalizations of Bernoulli numbers. These results are refinements of previously known ones.

      DOI: 10.1093/qmath/hap004

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    • On the zeros of Weng zeta functions for Chevalley groups Peer-reviewed

      Haseo Ki, Yasushi Komori, Masatoshi Suzuki

          20 11 2010

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      We prove that all but finitely many zeros of Weng's zeta function for a
      Chevalley group defined over $\Q$ are simple and on the critical line under
      some reasonable geometric hypothesis.

      DOI: 10.1007/s00229-015-0736-8

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    • Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and $q$-zeta functions Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

          16 6 2010

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      We consider certain double series of Eisenstein type involving
      hyperbolic-sine functions. We define certain generalized Hurwitz numbers, in
      terms of which we evaluate those double series. Our main results can be
      regarded as a certain generalization of well-known results of Hurwitz,
      Herglotz, Katayama and so on. Our results also include recent formulas of the
      third-named author which are double analogues of the formulas of Cauchy,
      Mellin, Ramanujan, Berndt and so on, about certain Dirichlet series involving
      hyperbolic functions. As an application, we give some evaluation formulas for
      $q$-zeta functions at positive integers.

      DOI: 10.1515/forum-2011-0300

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    • Functional equations and functional relations for the Euler double zeta-function and its generalization of Eisenstein type Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      PUBLICATIONES MATHEMATICAE-DEBRECEN77 ( 1-2 ) 15 - 31   6 2010

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:KOSSUTH LAJOS TUDOMANYEGYETEM  

      We consider certain double series in two variables such as the Euler double zeta-function and its generalization of Eisenstein type. In the former part, we give some functional equations among these series, which are Eisenstein type analogues of a previous result on double zeta-functions given by the second-named author. We point out that, on certain hyperplanes, we can show functional equations of traditional symmetric type for these double series. In the latter part, we give some functional relations for these series and double series of another type involving hyperbolic functions. As special cases, we can obtain the known value-relation formulas for these series given by the third-named author recently.

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    • On Witten multiple zeta-functions associated with semisimple Lie algebras II Peer-reviewed

      Yasushi KOMORI, Kohji MATSUMOTO, Hirofumi TSUMURA

      Journal of the Mathematical Society of Japan62 ( 2 ) 355 - 394   4 2010

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      Publishing type:Research paper (scientific journal)   Publisher:Mathematical Society of Japan (Project Euclid)  

      DOI: 10.2969/jmsj/06220355

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    • On multiple Bernoulli polynomials and multiple L-functions of root systems Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY100   303 - 347   3 2010

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:WILEY  

      We define generalized Bernoulli numbers, Bernoulli polynomials and multi-variable L-functions associated with root systems. We prove that the values of those L-functions at positive integers can be expressed in terms of those Bernoulli polynomials, and give an explicit formula for the latter. This result is a character analogue of Witten's volume formula for Witten's zeta-functions of semisimple Lie algebras. Furthermore, we show that the L-functions can be continued meromorphically to the whole space, and satisfy certain functional relations.

      DOI: 10.1112/plms/pdp025

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    • An introduction to the theory of zeta-functions of root systems Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      Algebraic and Analytic Aspects of Zeta Functions and $L$-functions   115 - 140   2010

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      Publishing type:Part of collection (book)   Publisher:The Mathematical Society of Japan  

      DOI: 10.2969/msjmemoirs/02101c060

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    • FUNCTIONAL RELATIONS FOR ZETA-FUNCTIONS OF ROOT SYSTEMS Peer-reviewed

      YASUSHI KOMORI, KOHJI MATSUMOTO, HIROFUMI TSUMURA

      Number Theory   11 2009

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      Publishing type:Research paper (international conference proceedings)   Publisher:WORLD SCIENTIFIC  

      DOI: 10.1142/9789814289924_0007

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    • Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications Peer-reviewed

      Yasushi Komori, Masatoshi Noumi, Jun'ichi Shiraishi

      SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS5   2009

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      Language:English   Publisher:NATL ACAD SCI UKRAINE, INST MATH  

      A unified approach is given to kernel functions which intertwine Ruijsenaars
      difference operators of type A and of type BC. As an application of the
      trigonometric cases, new explicit formulas for Koornwinder polynomials attached
      to single columns and single rows are derived.

      DOI: 10.3842/SIGMA.2009.054

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    • An integral representation of the Mordell-Tornheim double zeta function and its values at non-positive integers Peer-reviewed

      Yasushi Komori

      RAMANUJAN JOURNAL17 ( 2 ) 163 - 183   11 2008

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

      A surface integral representation of the Mordell-Tornheim double zeta function is given, which is a direct analogue of a well-known integral representation of the Riemann zeta function of Hankel's type. As an application, we investigate its values and residues at integers, where generalizations of a generating function of Bernoulli numbers naturally appear.

      DOI: 10.1007/s11139-008-9130-4

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    • Zeta and L-functions and Bernoulli polynomials of root systems Peer-reviewed

      Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

      PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES84 ( 5 ) 57 - 62   5 2008

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:JAPAN ACAD  

      This article is essentially an announcement of the papers [7-10] of the authors, though some of the examples are not included in those papers. We consider what is called zeta and L-functions of root systems which can be regarded as a multi-variable version of Witten multiple zeta and L-functions. Furthermore, corresponding to these functions, Bernoulli polynomials of root systems are defined. First we state several analytic properties, such as analytic continuation and location of singularities of these functions. Secondly we generalize the Bernoulli polynomials and give some expressions of values of zeta and L-functions of root systems in terms of these polynomials. Finally we give some functional relations among them by our previous method. These relations include the known formulas for their special values formulated by Zagier based on Witten's work.

      DOI: 10.3792/pjaa.84.57

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    • Zeta Functions of Root Systems Peer-reviewed

      Y. KOMORI, K. MATSUMOTO, H. TSUMURA

      The Conference on L-Functions   115 - 140   12 2006

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      Publishing type:Part of collection (book)   Publisher:WORLD SCIENTIFIC  

      DOI: 10.1142/9789812772398_0007

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    • Elliptic Ruijsenaars operators and functional equations Peer-reviewed

      Yasushi Komori

      Journal of Mathematical Physics43 ( 11 ) 5637 - 5653   11 2002

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      Publishing type:Research paper (scientific journal)   Publisher:AIP Publishing  

      DOI: 10.1063/1.1507604

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    • Symmetrization of nonsymmetric Macdonald polynomials and Macdonald's inner product identities Peer-reviewed

      A Nishino, Y Komori, H Ujino, M Wadati

      STUDIES IN APPLIED MATHEMATICS108 ( 4 ) 399 - 425   5 2002

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:BLACKWELL PUBLISHERS  

      We study the Macdonald polynomials that give eigenstates of some quantum many-body system with long-range interactions. Scalar products of the nonsymmetric Macdonald polynomials are algebraically evaluated through their Rodrigues-type formulas. We present a new proof of Macdonald's inner product identities without recourse to the shift operators; that is, we calculate square norms of the Macdonald polynomials through Weyl-symmetrization of those of the nonsymmetric Macdonald polynomials.

      DOI: 10.1111/1467-9590.01431

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    • The Perturbation of the Quantum Calogero-Moser-Sutherland System and Related Results Peer-reviewed

      Yasushi Komori, Kouichi Takemura

      Communications in Mathematical Physics227 ( 1 ) 93 - 118   1 5 2002

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      Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

      DOI: 10.1007/s002200200622

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      Other Link: http://link.springer.com/article/10.1007/s002200200622/fulltext.html

    • An algebraic approach to Macdonald–Koornwinder polynomials: Rodrigues-type formula and inner product identity Peer-reviewed

      Akinori Nishino, Yasushi Komori

      Journal of Mathematical Physics42 ( 10 ) 5020 - 5046   10 2001

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      Publishing type:Research paper (scientific journal)   Publisher:AIP Publishing  

      DOI: 10.1063/1.1398334

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    • Essential self-adjointness of the elliptic Ruijsenaars models Peer-reviewed

      Yasushi Komori

      Journal of Mathematical Physics42 ( 9 ) 4523 - 4553   9 2001

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      Publishing type:Research paper (scientific journal)   Publisher:AIP Publishing  

      DOI: 10.1063/1.1387271

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    • Ruijsenaars’ commuting difference operators and invariant subspace spanned by theta functions Peer-reviewed

      Yasushi Komori

      Journal of Mathematical Physics42 ( 9 ) 4503 - 4522   9 2001

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:AIP Publishing  

      We study a family of mutually commutative difference operators introduced by Ruijsenaars. The conjugations of these operators with an appropriate function give the Hamiltonians of some relativistic quantum systems. These operators can be regarded as elliptic analogs of the Macdonald operators and their coefficients consist of the Jacobi theta functions. We show that these operators act on the space of meromorphic functions on the Cartan subalgebra of affine Lie algebras and that the space spanned by characters of a fixed positive level is invariant under the action of these operators. (C) 2001 American Institute of Physics.

      DOI: 10.1063/1.1387449

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    • Symmetric and Non-symmetric Bases of Quantum Integrable Particle Systems with Long-Range Interactions Peer-reviewed

      Miki Wadati, Akinori Nishino, Hideaki Ujino, Yasushi Komori

      Journal of Statistical Physics102 ( 3/4 ) 1049 - 1064   2001

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      Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

      DOI: 10.1023/a:1004875625099

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    • Rodrigues formulas for the non-symmetric multivariable polynomials associated with the BCN-type root system Peer-reviewed

      Akinori Nishino, Hideaki Ujino, Yasushi Komori, Miki Wadati

      Nuclear Physics B571 ( 3 ) 632 - 648   4 2000

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      Publishing type:Research paper (scientific journal)   Publisher:Elsevier BV  

      DOI: 10.1016/s0550-3213(99)00761-0

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    • Theta Functions Associated with Affine Root Systems and the Elliptic Ruijsenaars Operators Peer-reviewed

      Yasushi Komori

      Physical Combinatorics   141 - 162   2000

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      Publishing type:Part of collection (book)   Publisher:Birkhäuser Boston  

      We study a family of mutually commutative difference operators associated
      with the affine root systems. These operators act on the space of meromorphic
      functions on the Cartan subalgebra of the affine Lie algebra. We show that the
      space spanned by the characters of a fixed positive level is invariant under
      the action of these operators.

      DOI: 10.1007/978-1-4612-1378-9_4

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    • Crystallization of the Bogoyavlensky Lattice Peer-reviewed

      Kazuhiro Hikami, Rei Inoue, Yasushi Komori

      Journal of the Physical Society of Japan68 ( 7 ) 2234 - 2240   15 7 1999

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Physical Society of Japan  

      We introduce a vertex model in two-dimension, which is associated withthe Bogoyavlensky lattice.We show that in a crystallized limit (q→0)we have a unique configuration, and that it coincides with anevolution of the soliton cellular automata which is a generalizationof the system introduced by Takahashi and Satsuma.

      DOI: 10.1143/jpsj.68.2234

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    • Diagonalization of the Elliptic Ruijsenaars Model of Type-$BC$ Peer-reviewed

      Kazuhiro Hikami, Yasushi Komori

      Journal of the Physical Society of Japan67 ( 12 ) 4037 - 4044   15 12 1998

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Physical Society of Japan  

      We study the elliptic Ruijsenaars model of type-BC, which is adifference analogue of the BC-type Calogero–Sutherland–Moser modelwith an elliptic pairwise potential.In the trigonometric limit, the difference operator of this model reduces to the Macdonald–Koornwinder operatorby a gauge-transformation.We show that our difference operatoracts on a finite-dimensional space of functions in a special case of thecoupling constant.

      DOI: 10.1143/jpsj.67.4037

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    • Conserved operators of the generalized elliptic Ruijsenaars models Peer-reviewed

      Yasushi Komori, Kazuhiro Hikami

      Journal of Mathematical Physics39 ( 11 ) 6175 - 6190   11 1998

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      Publishing type:Research paper (scientific journal)   Publisher:AIP Publishing  

      DOI: 10.1063/1.532622

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    • Diagonalization of the elliptic Ruijsenaars model. Correspondence with the Belavin model Peer-reviewed

      K. Hikami, Y. Komori

      The European Physical Journal B5 ( 3 ) 583 - 588   10 1998

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      Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

      DOI: 10.1007/s100510050482

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      Other Link: http://link.springer.com/article/10.1007/s100510050482/fulltext.html

    • Boundary Boltzmann Weight for the Eight-Vertex SOS Model: Vertex-IRF Correspondence Peer-reviewed

      Kazuhiro Hikami, Yasushi Komori

      Journal of the Physical Society of Japan67 ( 1 ) 78 - 82   15 1 1998

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Physical Society of Japan  

      Integrable boundary Boltzmann weight for the eight-vertexsolid-on-solid model is constructed.Based on the operator-valued solutions of both the Yang-Baxterequation and the reflection equation,we propose a simple method to give the Boltzmann weight using thevertex-IRF correspondence.

      DOI: 10.1143/jpsj.67.78

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    • Affine $R$-matrix and the Generalized Elliptic Ruijsenaars Models Peer-reviewed

      Yasushi Komori, Kazuhiro Hikami

      Letters in Mathematical Physics43 ( 4 ) 335 - 346   1998

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      Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

      DOI: 10.1023/a:1007452800428

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    • Notes on the Elliptic Ruijsenaars Operators Peer-reviewed

      Yasushi Komori

      Letters in Mathematical Physics46 ( 2 ) 147 - 155   1998

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      Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

      DOI: 10.1023/a:1007577231399

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    • Nonlinear Schrödinger Model with Boundary, Integrability and Scattering Matrix Based on the Degenerate Affine Hecke Algebra Peer-reviewed

      Yasushi Komori, Kazuhiro Hikami

      International Journal of Modern Physics A12 ( 30 ) 5397 - 5410   10 12 1997

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      Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

      The δ-function interacting many-body systems (nonlinear Schrödinger models) on an infinite interval and with boundary are studied by use of the integrable differential-difference operators, so-called Dunkl operators. These models are related with the classical root systems of type A and BC, and we give a systematic method to construct these integrable operators. This method is based on the infinite-dimensional representation for solutions of the classical Yang–Baxter equation and the classical reflection equation. In addition the scattering matrices of the boundary nonlinear Schrödinger model are investigated.

      DOI: 10.1142/s0217751x97002887

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    • Elliptic $K$-matrix associated with Belavin's symmetric $R$-matrix Peer-reviewed

      Yasushi Komori, Kazuhiro Hikami

      Nuclear Physics B494 ( 3 ) 687 - 701   6 1997

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      Publishing type:Research paper (scientific journal)   Publisher:Elsevier BV  

      DOI: 10.1016/s0550-3213(97)00177-6

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    • Integrability, Fusion, and Duality in the Elliptic Ruijsenaars Model Peer-reviewed

      Kazuhiro Hikami, Yasushi Komori

      Modern Physics Letters A12 ( 11 ) 751 - 761   10 4 1997

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      Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

      The generalized elliptic Ruijsenaars models, which are regarded as a difference analog of the Calogero–Sutherland–Moser models associated with the classical root systems are studied. The integrability and the duality using the fusion procedure of operator-valued solutions of the Yang–Baxter equation and the reflection equation are shown. In particular a new integrable difference operator of type-D is proposed. The trigonometric models are also considered in terms of the representation of the affine Hecke algebra.

      DOI: 10.1142/s0217732397000789

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    • Integrable three-body problems with two- and three-body interactions Peer-reviewed

      Yasushi Komori, Kazuhiro Hikami

      Journal of Physics A: Mathematical and General30 ( 6 ) 1913 - 1923   21 3 1997

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      Publishing type:Research paper (scientific journal)   Publisher:IOP Publishing  

      DOI: 10.1088/0305-4470/30/6/017

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    • Quantum Integrability of the Generalized Elliptic Ruijsenaars Models Peer-reviewed

      Y. Komori, K. Hikami

      Journal of Physics A30   4341 - 4364   1997

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    • NOTES ON OPERATOR-VALUED SOLUTIONS OF THE YANG-BAXTER EQUATION AND THE REFLECTION EQUATION Peer-reviewed

      KAZUHIRO HIKAMI, YASUSHI KOMORI

      Modern Physics Letters A11 ( 36 ) 2861 - 2870   30 11 1996

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      Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

      We reconsider the operator-valued solutions of the Yang-Baxter equation and the reflection equation. We construct quantum Knizhnik-Zamolodchikov type operators, and discussed the relationship with the MacDonald q-polynomial theory associated with the classical root systems.

      DOI: 10.1142/s0217732396002848

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    • Bethe ansatz wavefunctions and an infinite number of conserved operators of the Luttinger model Peer-reviewed

      Yasushi Komori, Miki Wadati

      Physics Letters A218 ( 1-2 ) 42 - 48   7 1996

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      Publishing type:Research paper (scientific journal)   Publisher:Elsevier BV  

      DOI: 10.1016/0375-9601(96)00385-4

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    • Massless Thirring Model and Bethe Ansatz Wavefunction Peer-reviewed

      Yasushi Komori, Miki Wadati

      Journal of the Physical Society of Japan65 ( 3 ) 722 - 724   15 3 1996

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      Language:English   Publishing type:Research paper (scientific journal)   Publisher:Physical Society of Japan  

      The quantum one-dimensional massless Thirring model is studied. A transformation which casts the massless Thirring model into a quadratic form is found. The transformed field operators satisfy interesting commutation relations, fermion anti-commutation relations among the same kinds of fields and anyon-like commutation relations between different kinds. Bethe Ansatz wavefunctions are constructed algebraically using the transformation and the commutation relations in coordinate space.

      DOI: 10.1143/jpsj.65.722

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    Misc.

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    Presentations

    • 有限多重ゼータ値, 対称多重ゼータ値, および補間ゼータ関数について Invited

      小森 靖

      多重ゼータ研究集会  16 2 2020 

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      Venue:近畿大学  

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    • Finite Multiple Zeta Values, Symmetric Multiple Zeta Values and Unified Multiple Zeta Functions Invited

      小森 靖

      愛媛大学代数セミナー  20 12 2019 

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      Venue:愛媛大学  

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    • Finite Multiple Zeta Values, Multiple Zeta Functions and Multiple Bernoulli Polynomials Invited

      小森 靖

      九大多重ゼータセミナー  18 6 2018 

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      Venue:九州大学  

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    • 多重楕円ガンマ関数の積分表示と関数関係式 Invited

      小森 靖

      多重三角関数とその一般化  5 2 2018 

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      Venue:神戸大学  

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    • Functional relations for zeta-functions of root systems and Poincar\'e polynomials of Weyl groups I Invited

      Y. Komori

      Various Aspects of Multiple Zeta Functions  2017 

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      Venue:名古屋大学  

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    • 荒川・金子ゼータ関数の $\mathrm{GL}_2(\mathbb{C})$ 拡張とその関数関係式について Invited

      小森 靖

      関西多重ゼータ研究会  3 12 2016 

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      Venue:大阪大学  

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    • Zeta-functions of root systems and Poincar\'e polynomials of Weyl groups

      Y. Komori

      Problems and Prospects in Analytic Number Theory  31 10 2016 

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      Venue:京都大学  

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    • On Arakawa-Kaneko zeta-functions associated with $\mathrm{GL}_2(\mathbb{C})$ and their functional relations

      小森 靖

      解析数論セミナー  17 6 2016 

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      Venue:名古屋大学  

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    • 超平面配置の格子和とその応用 Invited

      小森 靖

      関西多重ゼータ研究会  17 10 2015 

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      Venue:立命館大学  

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    • Lattice sums of hyperplane arrangements and their applications

      Y. Komori

      French-Japanese Workshop on multiple zeta functions and applications  7 9 2015 

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      Venue:St-Etienne  

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    • 多重ゼータ関数の積分表示と非正整数点での漸近挙動

      小森 靖

      解析数論セミナー  27 2 2014 

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      Venue:名古屋大学  

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    • ルート系に付随する多重ゼータ関数について Invited

      小森 靖

      大岡山談話会  20 11 2013 

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      Venue:東京工業大学  

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    • Desingularization of complex multiple zeta-functions and fundamentals of $p$-adic multiple $L$-functions I Invited

      Y. Komori

      2013 多重ゼータ値の諸相  24 7 2013 

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      Venue:京都大学  

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    • ルート系に付随する多重ゼータ関数について

      小森 靖

      立教大学数理物理学研究センター第13回セミナー  5 12 2012 

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      Venue:立教大学  

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    • Zeta-functions of weight lattices of compact connected semisimple Lie groups Invited

      Y. Komori

      2012 Conference on $L$-functions  24 8 2012 

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      Venue:Jeju  

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    • ルート系と多重ゼータ関数について Invited

      小森 靖

      第5回多重ゼータおよびその周辺  27 1 2012 

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      Venue:九州大学  

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    • Witten ゼータ関数入門 (II) Invited

      小森 靖

      関西多重ゼータ研究会  21 1 2012 

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      Venue:大阪工業大学  

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    • ルート系のゼータ関数とベルヌーイ関数 (I) Invited

      小森 靖

      明学セミナー  10 12 2011 

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      Venue:明治学院大学  

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    • Euler Zagier zeta-functions and zeta-functions of root systems

      Y. Komori

      14 9 2011 

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      Venue:Wuerzburg  

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    • Zeta-functions of root systems and of Lie groups

      Y. Komori

      7 9 2011 

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      Venue:Palanga  

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    • リー群に付随するゼータ関数について Invited

      小森 靖

      第4回ゼータ若手研究集会  21 2 2011 

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      Venue:沖縄県青年会館  

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    • 連結半単純コンパクトリー群に付随するゼータ関数について Invited

      小森 靖

      2010年度表現論シンポジウム  10 11 2010 

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      Venue:公共の宿おおとり荘  

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    • ルート系のゼータ関数と多重ゼータ値 I Invited

      小森 靖

      多重ゼータ値の諸相  8 9 2010 

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      Venue:京都大学  

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    • Multiple Bernoulli polynomials and multiple $L$-functions of root systems Invited

      Y. Komori

      Developments in Quantum Integrable Systems  14 6 2010 

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      Venue:京都大学  

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    • $(G,P)$ に付随する Weng ゼータ関数の関数等式について

      小森 靖

      代数的整数論とその周辺  9 12 2009 

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      Venue:東京大学  

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    • Multiple Bernoulli polynomials and multiple $L$-functions of root systems Invited

      Y. Komori

      l'atelier Zeta III  23 11 2009 

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      Venue:Univ. Jean-Monnet  

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    • ルート系の多重ベルヌーイ多項式と多重 $L$ 関数について

      小森 靖

      数学談話会  10 9 2009 

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      Venue:愛媛大学  

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    • ルート系の多重ベルヌーイ多項式と多重 $L$ 関数について Invited

      小森 靖

      表現論と組合せ論  27 8 2009 

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      Venue:北海道大学  

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    • Functional equations for Weng's zeta functions for $(G,P)$ Invited

      小森 靖

      代数学セミナー  19 6 2009 

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      Venue:九州大学  

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    • Functional equations for Weng's zeta functions for $(G,P)$

      小森 靖

      代数学解析数論セミナーセミナー  17 6 2009 

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      Venue:名古屋大学  

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    • Hurwitz-Lerch 多重ゼータ関数の面積分表示と多重ベルヌーイ数

      小森 靖

      日本数学会年会  27 3 2009 

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      Venue:東京大学  

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    • Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems

      小森 靖;松本耕二;津村博文

      日本数学会年会  27 3 2009 

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      Venue:東京大学  

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    • Multiple Bernoulli polynomials and multiple $L$-functions of root systems

      Y. Komori

      Oberseminar ZAHLENTHEORIE  27 11 2008 

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      Venue:Weurzburg Univ.  

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    • Certain double series of Euler type and of Eisenstein type and Hurwitz numbers (I)

      Y. Komori; K.Matsumoto;H. Tsumura

      New Aspects of Analytic Number Theory  29 10 2008 

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      Venue:京都大学  

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    • Certain double series of Euler type and of Eisenstein type and Hurwitz numbers (II)

      Y. Komori; K.Matsumoto;H. Tsumura

      New Aspects of Analytic Number Theory  29 10 2008 

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      Venue:京都大学  

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    • Multiple Bernoulli polynomials and multiple zeta functions of root systems Invited

      Y. Komori

      Elliptic integrable systems, isomonodromy problems, and hypergeometric functions 

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      Event date: 21 7 2008 - 25 7 2008

      Venue:Max Planck Institute for Mathematics  

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    • 多重ゼータ関数の積分表示と多重ベルヌーイ数

      小森 靖

      整数論セミナー  12 6 2008 

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      Venue:津田塾大学  

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    • Multiple Bernoulli polynomials and multiple $L$-functions of root systems Invited

      Y. Komori; K.Matsumoto;H. Tsumura

      French-Japanese Winter School on Zeta and $L$-functions  9 1 2008 

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      Venue:マホロバマインズ 三浦海岸  

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    • 多重ゼータ関数の積分表示について

      小森 靖

      解析数論セミナー  19 12 2007 

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      Venue:名古屋大学  

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    • An integral representation of multiple zeta-functions

      Y. Komori

      Journ\'ees autour des series de Dirichlet  13 11 2007 

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      Venue:Univ. Lille 1  

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    • On multiple Bernoulli polynomials and multiple $L$-functions of root systems

      Y. Komori, K. Matsumoto, H. Tsumura

      Analytic Number Theory and Related Areas  19 10 2007 

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      Venue:京都大学  

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    • ルート系に付随した多重ゼータ関数とベルヌーイ多項式 Invited

      小森 靖

      東京無限可積分系セミナー  21 10 2006 

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      Venue:東京大学  

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    • Mordell-Tornheim 二重ゼータ関数の積分表示と非正整数点での値

      小森 靖

      解析数論セミナー  17 4 2006 

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      Venue:名古屋大学  

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    • ルート系に付随する Calogero-Sutherland 模型と Ruijsenaars 模型 Invited

      小森 靖

      ソリトン理論から可積分数理へ 

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      Event date: 22 8 2005 - 24 8 2005

      Venue:京都大学  

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    • Elliptic Gamma function and its properties

      小森 靖

      解析数論セミナー  16 5 2005 

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      Venue:名古屋大学  

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    • Macdonald Operators and Root Systems Invited

      小森 靖

      複素鏡映群に付随した Hecke 環と Macdonald 関数  30 11 2004 

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      Venue:名古屋大学  

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    • Elliptic Ruijsenaars operators and elliptic hypergeometric integrals

      Y. Komori

      楕円可積分系の研究 

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      Event date: 8 11 2004 - 11 11 2004

      Venue:京都大学  

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    • 多重楕円ガンマ関数のモジュラー変換性

      小森 靖;野海 正俊

      日本数学会秋季総合分科会 

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      Event date: 19 9 2004 - 22 9 2004

      Venue:北海道大学  

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    • 楕円型 Ruijsenaars 差分作用素と楕円超幾何積分

      小森 靖;野海 正俊

      日本数学会秋季総合分科会 

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      Event date: 19 9 2004 - 22 9 2004

      Venue:北海道大学  

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    • Elliptic Ruijsenaars operators and elliptic hypergeometric integrals Invited

      Y. Komori

      可解格子模型の最近の進展 

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      Event date: 20 7 2004 - 23 7 2004

      Venue:京都大学  

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    • Construction and properties of elliptic difference Ruijsenaars operators

      小森 靖

      神戸可積分セミナー  12 6 2003 

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      Venue:神戸大学  

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    • ルート系に付随する Macdonald-Ruijsenaars 差分作用素について Invited

      小森 靖

      表現論セミナー  18 11 2002 

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      Venue:岡山理科大学  

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    • 楕円型 Macdonald-Ruijsenaars 差分作用素とルート系 Invited

      小森 靖

      日本数学会年会 

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      Event date: 28 3 2002 - 31 3 2002

      Venue:明治大学  

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    • 楕円型 Ruijsenaars 模型の保存量について

      小森 靖

      東京無限可積分セミナー 

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      Event date: 25 9 2001 - 28 9 2001

      Venue:新潟県小千谷市木津の湯  

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    • アフィンリー代数の指標と楕円型 Ruijsenaars 模型

      小森 靖

      Quantum Integrable Models  3 2001 

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      Venue:京都大学  

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    • Essential self-adjointness of the elliptic Ruijsenaars models

      Y. Komori

      11 2000 

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      Venue:早稲田大学  

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    • 一般化された Sutherland 模型のボソン的, フェルミオン的固有状態

      西野 晃徳, 小森 靖, 宇治野 秀晃, 和達 三樹

      日本物理学会第55回年会  9 2000 

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      Venue:新潟大学  

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    • Yang-Baxter equation and elliptic Ruijsenaars model

      Y. Komori

      3 2000 

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      Venue:Colorado Univ.  

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    • $BC_N$ 型サザーランド模型に付随する非対称多変数多項式

      西野 晃徳, 宇治野 秀晃, 小森 靖, 和達 三樹

      日本物理学会2000年春の分科会  3 2000 

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      Venue:関西大学  

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    • Yang-Baxter equation and elliptic Ruijsenaars model

      Y. Komori

      3 2000 

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      Venue:CRM, Montreal Univ.  

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    • アフィンリー代数の指標と楕円型 Ruijsenaars 模型

      小森 靖

      非線形波動のメカニズム -現象とモデルの数理構造  11 1999 

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      Venue:九州大学  

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    • $BC_N$ 型ルート系に付随する非対称多変数多項式

      西野 晃徳, 宇治野 秀晃, 小森 靖

      非線形波動のメカニズム -現象とモデルの数理構造  11 1999 

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      Venue:九州大学  

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    • 楕円型 Ruijsenaars operator の作用する空間と自己共役性

      小森 靖, 樋上 和弘, 和達 三樹

      日本物理学会第54回年会  3 1999 

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      Venue:広島大学  

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    • Affine root systems and the elliptic Ruijsenaars models

      小森 靖

      Physical Combinatorics  1 1999 

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      Venue:京都大学  

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    • アフィン $R$ 行列と Ruijsenaars 模型

      小森 靖, 樋上 和弘, 和達 三樹

      日本物理学会秋の分科会  9 1998 

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      Venue:琉球大学  

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    • Affine $R$-matrix and the generalized elliptic Ruijsenaars models

      Y. Komori

      STATPHYS 20  7 1998 

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    • 八頂点模型と可積分境界条件

      小森 靖, 樋上 和弘, 和達 三樹

      日本物理学会秋の分科会  9 1997 

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      Venue:神戸大学  

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    • $Z_n$ バクスター模型と可積分境界条件

      小森 靖, 樋上 和弘, 和達 三樹

      日本物理学会第52回年会  3 1997 

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      Venue:名城大学  

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    • 境界のあるデルタ関数型相互作用系の可積分性と $S$ 行列

      小森 靖, 樋上 和弘, 和達 三樹

      日本物理学会秋の分科会  9 1996 

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      Venue:山口大学  

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    • Transformation of the Luttinger model into a quadratic form

      小森 靖, 和達 三樹

      日本物理学会第51回年会  3 1996 

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      Venue:金沢大学  

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    Research Projects

    • 種々の多重ゼータ値における有限類似と対称類似の統一理論の構築

      日本学術振興会  科学研究費助成事業 基盤研究(C) 

      小森 靖

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      4 2021 - 3 2026

      Grant number:21K03189

      Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

      有限多重ゼータ値と対称多重ゼータ値において, 現在最も重要な研究目標とされている金子・Zagier 予想に関して進展が得られた. これは多重ゼータ値を定義する級数を有限で打ち切って有限体上の数列とみなす有限多重ゼータ値と, 通常の多重ゼータ値のある種の対称化である対称多重ゼータ値の間には一対一対応があるという予想である. この予想に対し統一多重ゼータ関数という新しい対象を導入し, これらのゼータ値がある意味で同一の対象であることを示した. 統一多重ゼータ関数とは通常の多重ゼータ関数が持つ複素変数の他, 体の標数を滑らかに補間する2つの複素変数を添加したものであり, 特殊化することによって有限多重ゼータ値, 対称多重ゼータ値, 通常の多重ゼータ値, 及び更なる拡張である有限多重ゼータ値の p 進化, 対称多重ゼータ値の t 進化を全て得ることができる. この研究は「なぜ同型が存在するか」という本質的な問いに対して「1つの対象の異なる見方だから」という方向性の解答を提案するものである. これを持って直ちに予想が解決するわけではないが, これまで独立に扱われていた対象が極めて自然に1つに統合されたことにより今後の研究に大きな影響を与えるものと考えられる. この成果の一つとして, 負の領域における金子・Zagier 予想 (1対1対応部分) を肯定的に解決した. 現在さらにモーデルトーンハイム型多重ゼータ値やルート系に付随する有限多重ゼータ値に対して同様な現象が起こることを確認し, その証明を考察中である.

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    • The analytic theory of arithmetic L-functions and multiple zeta-functions

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B) 

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      4 2018 - 3 2022

      Grant number:18H01111

      Grant amount:\14560000 ( Direct Cost: \11200000 、 Indirect Cost:\3360000 )

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    • 多重ゼータ関数の総合的研究と量子可積分系への応用

      日本学術振興会  科学研究費助成事業 基盤研究(C) 

      小森 靖

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      4 2017 - 3 2021

      Grant number:17K05185

      Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

      2018 年度は, 前年度に行ったリー群に付随する多重ゼータ関数の関係式を記述する母関数の構成について, 論文を作成し投稿した. 具体的には古典ルート型である A,B,C,D 型ルート系の各々の場合において, ランクが 1 つ小さい同じ型の部分ルート系に付随する関数関係式の母関数を全て得ているが, これらのうち B,D と A1 × A1 に関する部分についてまとめた. これで基本理論は一つの区切りを迎えたと感じている. 現在これまでの研究成果をまとめて, 本として出版する予定を立てており, それに向けての作業を始めている段階である. なお, 今後さらなる一般化の考察も同時並行で行っていく予定である. (松本耕二氏 (名古屋大), 津村博文氏 (首都大) との共同研究)
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      また, 当初の計画にはなかったこととして, 有限多重ゼータ値の母関数についての研究を行った. 近年, 多重ゼータ値を定義する級数を有限で打ち切って有限体上の数列とみなす有限多重ゼータ値の研究が注目を集めている. これらは通常の多重ゼータ値と一対一対応があると予想されており, その値を求めることは大変興味深い. この問題に対し, ファウルハーバーの公式を一般化することで記述する方法を見出し, 値の母関数を構成することに成功した. 特に負の領域では全て 0 になることを証明した. 今後この母関数を調べることによって, 多重ゼータ値に対して新しい知見が得られることが期待できる.

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    • Research on number theoretic properties of zeta functions in several variables

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) 

      TSUMURA Hirofumi, MATSUMOTO Kohji, KOMORI Yasushi, FURUSHO Hidekazu

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      4 2015 - 3 2018

      Grant number:15K04788

      Grant amount:\4680000 ( Direct Cost: \3600000 、 Indirect Cost:\1080000 )

      The main aim in this research is to study what is called the zeta function which plays an important role in number theory and investigate their properties. In particular, we studied zeta functions in several variables mainly from the viewpoint of the analytic aspect. We studied the Witten zeta function in several variables which was defined based on Witten's work, and also the Arakawa-Kaneko zeta function defined by Tsuneo Arakawa and Masanobu Kaneko. Our main result is consider the number theoretic properties of these zeta functions,and consequently we obtained unknown properties of them and gave new results.

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    • A study on algebraic and analytic behavior of multiple zeta-functions and multiple automorphic L-functions

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B) 

      Matsumoto Kohji, TSUMURA HIROFUMI, KANEKO MASANOBU, OHNO YASUO, SHOJI MAYUMI, FURUSHO HIDEKAZU, YAMASAKI YOSHINORI, UMEGAKI YUMIKO, NAKAMURA TAKASHI

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      4 2013 - 3 2018

      Grant number:25287002

      Grant amount:\18070000 ( Direct Cost: \13900000 、 Indirect Cost:\4170000 )

      The present research has dealt with various multiple series, such as multiple zeta-functions of Euler-Zagier type, a more general class of zeta-functions of root systems, and also the same type of series with Fourier coefficients of modular forms on the numerators. The main results obtained in the period of the present research are the structure theory and functional relations for zeta-functions of root systems, or more general multiple zeta-functions associated with Lie groups; evaluation of values of multiple series involving hyperbolic functions; numerical computations on the zeros multiple zeta-functions; the proof of two types of functional equations for double zeta-functions involving Fourier coefficients of modular forms on the numerator; the idea of desingularized multiple zeta-functions and the development of the theory of p-adic multiple zeta-functions.

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    • Studies on quantum integrable systems and multiple zeta functions

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) 

      KOMORI Yasushi

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      4 2013 - 3 2017

      Grant number:25400026

      Grant amount:\4810000 ( Direct Cost: \3700000 、 Indirect Cost:\1110000 )

      Both partition functions in quantum gauge theories and zeta-functions in mathematics, which play fundamental and important roles in each area, happen to coincide in some cases. Among them are the Witten zeta-functions. These zeta-functions are the main objects and should be studied from various viewpoints. For this problem, we proposed lattice sums associated with hyperplane arrangements and established a unified way to treat these values and functional relations among Witten zeta-functions via their generating functions. We also studied some properties of related zeta-functions and hypergeometric functions, and obtained new functional relations and formulas.

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    • Explicit formulas of $p$-adic spherical functions and their applications

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) 

      Hironaka Yumiko, SATO FUMIHIRO, KOMORI YASUSHI, Rubenthaler Hubert, Boecherer Siegfried

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      4 2012 - 3 2016

      Grant number:24540031

      Grant amount:\4940000 ( Direct Cost: \3800000 、 Indirect Cost:\1140000 )

      We have investigated the spaces of unitary-hermitian matrices on the basis of spherical functions as $p$-adic homogeneous spaces. We may apply a general expression formula of spherical functions which the researcher got before. The present groups have different root systems according to the parity of the size of matrices, and the Cartan decomposition of the spaces have different shapes according to the residual characteristic of the base field. We have studied at first the odd residual and even-size space, then the other cases. Finally we have a unified description for the results.

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    • Studies on various multiple zeta-functions associated with root systems

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) 

      KOMORI Yasushi

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      4 2010 - 3 2014

      Grant number:22540045

      Grant amount:\3250000 ( Direct Cost: \2500000 、 Indirect Cost:\750000 )

      Both partition functions in quantum gauge theories and zeta-functions in mathematics, which play fundamental and important roles in each area, happen to coincide in some cases. Among them are the Witten zeta-functions. Special values of these zeta-functions at positive integers are the main objects and should be studied from various viewpoints. For this problem, we established a unified way to treat these values via their generating functions. We also obtained new functional relations and formulas for related zeta-functions and hypergeometric functions from the viewpoint of root systems.

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    • Research on arithmetic properties of multiple Dirichlet series

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) 

      TSUMURA Hirofumi, MATSUMOTO Kohji, KOMORI Yasushi

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      2011 - 2013

      Grant number:23540022

      Grant amount:\4940000 ( Direct Cost: \3800000 、 Indirect Cost:\1140000 )

      We study analytic properties of the multiple Dirichlet series from the various viewpoints. In particular, we obtain some value-relations and functional relations for them, and consider their applications to number theory. Concretely we study Witten's zeta-functions associated with the root systems and certain Eisenstein type series as a joint work with K. Matsumoto (Nagoya University) and Y. Komori (Rikkyo University). Our research is being completed as a fruitful theory. As for double zeta-functions, we obtain a new type of the mean value theorem. We greatly expect its application to number theory.

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    • Representation theory of algebraic groups, quantum groups and Hecke algebras

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A) 

      SHOJI Toshiaki, OKADA Soichi, IYAMA Osamu, ISHI Hideyuki, KOMORI Ysushi, MIYACHI Hyoe, NAGAO Kentaro, MIYACHI Hyoe, SHINODA Ken-ichi, TANISAKI Toshiyuki, KANEDA Masaharu, ATIKI Susumu, WADA Kentaro

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      2008 - 2012

      Grant number:20244001

      Grant amount:\36790000 ( Direct Cost: \28300000 、 Indirect Cost:\8490000 )

      Proved the Springer correspondence between the intersection cohomologies arising from the exotic nilpotent cone and irreducible characters of Weyl groups of type C. By using this, proved the conjecture of Achar-Henderson concerning with Poincare polynomials of such intersection cohomologies.

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    • Analytic structures and arithmetic properties of multiple zeta-functions

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B) 

      MATSUMOTO Kohji, KOMORI Yasushi, TSUMURA Hirofumi, KANEKO Masanobu, KANEMITSU Shigeru, EGAMI Shigeki, OCHIAI Hiroyuki, OHNO Yasuo, TANIGAWA Yoshio

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      2008 - 2012

      Grant number:20340003

      Grant amount:\19240000 ( Direct Cost: \14800000 、 Indirect Cost:\4440000 )

      We studied analytic properties, special values and their relations with actions of Weyl groups, and functional relations for multiple zeta-functions associated with root systems. We proved several new formulas. In particular, we obtained functional relations and parity results for the zeta-function of the root system of type G_2, new relations for Euler-Zagier sums from the viewpoint of root systems of type C, and various properties of more general zeta-functions associated with Lie groups.

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    • Multiple zeta functions associated with root systems and their applications

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B) 

      YASUSHI Komori

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      2007 - 2009

      Grant number:19740009

      Grant amount:\2880000 ( Direct Cost: \2400000 、 Indirect Cost:\480000 )

      In the quantum gauge theory, which is one of those describing nature, the partition functions are considered to be the most fundamental and important quantities. Witten found that certain limits of the partition functions are described in terms of the volumes of certain spaces. These can be regarded as special values of zeta functions. In this study, we derived general formulas which give these special values, and furthermore presented some solutions to related problems.

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    • 長距離相互作用を持つ一次元量子多体系の代数的解析とその応用

      日本学術振興会  科学研究費助成事業 若手研究(B) 

      小森 靖

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      2003 - 2005

      Grant number:15740235

      Grant amount:\3700000 ( Direct Cost: \3700000 )

      昨年度に引き続き、楕円型Ruijsenaars模型についての研究を進めた。量子模型については東京大学の坂井氏や、神戸大学の野海氏らの研究グループとの共同研究によって得られた楕円差分Painleve系とそれに付随する楕円超幾何方程式についての研究成果を基に、これまでに楕円テータ関数による級数解や、さらにパラメータを一般化したものにも適応可能な楕円ガンマ関数の積分によって記述される楕円超幾何積分の解を得ている。一方、一般ルート系において、対応する古典系についての研究はRuijsenaarsやvan DiejenらによるA,BC型の結果しか得られていなかった。そこで今年度は古典楕円型Ruijsenaars模型の可積分性について研究を行うこととした。その結果、系の自由度と同数の保存量の構成とそれらの関数としての独立性についての証明を行うことができた。これによって一般ルート系における楕円型Ruijsenaars模型の可積分性が示されたことになる。保存量の構成はvan Diejenが用いた方法による。具体的には量子古典対応によって量子論における可換差分作用素から古典極限を取るという方法を用いた。以前の研究によって、一般ルート系に付随する模型の可換差分作用素はルート代数と呼ばれる代数を用いて構成されることが明らかとなっている。この構成法とさらにルート系の性質をうまく使うことによって古典極限を取ることができた。また保存量の独立性についても可換差分作用素の構成時における作用素の"先頭項"に着目することによって示すことができた。この結果は既に京都大学数理解析研究所で2005年8月に行われた「ソリトン理論から可積分数理へ」で口頭発表済みである。

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    • 長距離相互作用を持つ一次元量子多体系の代数的解析とその応用

      日本学術振興会  科学研究費助成事業 特別研究員奨励費 

      小森 靖

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      2000 - 2001

      Grant number:00J08053

      Grant amount:\2400000 ( Direct Cost: \2400000 )

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    • 長距離相互作用を持つ一次元量子多体系

      日本学術振興会  科学研究費助成事業 特別研究員奨励費 

      小森 靖

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      1997 - 1999

      Grant number:97J07821

      Grant amount:\2700000 ( Direct Cost: \2700000 )

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    • Quantum Integrable Systems

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      4 1995

      Grant type:Competitive

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