掲載種別：研究論文（学術雑誌）   出版者・発行元：Mathematical Society of Japan (Project Euclid)  

DOI： 10.2969/jmsj/07017501

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掲載種別：研究論文（学術雑誌）   出版者・発行元：Project Muse  

DOI： 10.1353/ajm.2017.0002

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掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

DOI： 10.1007/s00029-016-0233-2

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その他リンク： http://link.springer.com/article/10.1007/s00029-016-0233-2/fulltext.html

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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その他リンク： http://link.springer.com/article/10.1007/s00365-015-9316-0/fulltext.html

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Cambridge University Press (CUP)  

<title>Abstract</title>We study the values of the zeta-function of the root system of type <italic>G</italic>₂ 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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掲載種別：研究論文（学術雑誌）   出版者・発行元：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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記述言語：英語   出版者・発行元：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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記述言語：英語  

DOI： 10.14992/00010883

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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記述言語：英語   出版者・発行元：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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記述言語：英語   出版者・発行元：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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記述言語：英語   出版者・発行元：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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記述言語：英語   掲載種別：論文集(書籍)内論文   出版者・発行元：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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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その他リンク： http://link.springer.com/article/10.1007/s00209-010-0705-6/fulltext.html

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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記述言語：英語   出版者・発行元：立教大学  

CiNii Article

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：RESEARCH INST MATHEMATICAL SCIENCES, KYOTO UNIV  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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>₂, <italic>A</italic>₃, <italic>B</italic>₂, <italic>B</italic>₃ and <italic>C</italic>₃. In this paper, we consider the case of <italic>G</italic>₂-type. We define certain analogues of Bernoulli polynomials of <italic>G</italic>₂-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of <italic>G</italic>₂-type. Next, we consider the meromorphic continuation of the zeta-function of <italic>G</italic>₂-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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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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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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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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掲載種別：研究論文（学術雑誌）   出版者・発行元：Mathematical Society of Japan (Project Euclid)  

DOI： 10.2969/jmsj/06220355

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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掲載種別：論文集(書籍)内論文   出版者・発行元：The Mathematical Society of Japan  

DOI： 10.2969/msjmemoirs/02101c060

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掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：WORLD SCIENTIFIC  

DOI： 10.1142/9789814289924_0007

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記述言語：英語   出版者・発行元：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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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掲載種別：論文集(書籍)内論文   出版者・発行元：WORLD SCIENTIFIC  

DOI： 10.1142/9789812772398_0007

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掲載種別：研究論文（学術雑誌）   出版者・発行元：AIP Publishing  

DOI： 10.1063/1.1507604

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

DOI： 10.1007/s002200200622

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その他リンク： http://link.springer.com/article/10.1007/s002200200622/fulltext.html

掲載種別：研究論文（学術雑誌）   出版者・発行元：AIP Publishing  

DOI： 10.1063/1.1398334

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掲載種別：研究論文（学術雑誌）   出版者・発行元：AIP Publishing  

DOI： 10.1063/1.1387271

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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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掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

DOI： 10.1023/a:1004875625099

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掲載種別：研究論文（学術雑誌）   出版者・発行元：Elsevier BV  

DOI： 10.1016/s0550-3213(99)00761-0

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掲載種別：論文集(書籍)内論文   出版者・発行元：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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人日本物理学会  

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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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人日本物理学会  

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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掲載種別：研究論文（学術雑誌）   出版者・発行元：AIP Publishing  

DOI： 10.1063/1.532622

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掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

DOI： 10.1007/s100510050482

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その他リンク： http://link.springer.com/article/10.1007/s100510050482/fulltext.html

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人日本物理学会  

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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掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

DOI： 10.1023/a:1007452800428

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掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC  

DOI： 10.1023/a:1007577231399

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掲載種別：研究論文（学術雑誌）   出版者・発行元：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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掲載種別：研究論文（学術雑誌）   出版者・発行元：Elsevier BV  

DOI： 10.1016/s0550-3213(97)00177-6

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掲載種別：研究論文（学術雑誌）   出版者・発行元：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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掲載種別：研究論文（学術雑誌）   出版者・発行元：IOP Publishing  

DOI： 10.1088/0305-4470/30/6/017

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掲載種別：研究論文（学術雑誌）   出版者・発行元：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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掲載種別：研究論文（学術雑誌）   出版者・発行元：Elsevier BV  

DOI： 10.1016/0375-9601(96)00385-4

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人日本物理学会  

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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記述言語：英語   出版者・発行元：京都大学  

CiNii Article

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その他リンク： http://hdl.handle.net/2433/58038

記述言語：日本語   出版者・発行元：京都大学  

CiNii Article

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その他リンク： http://hdl.handle.net/2433/48156

記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

CiNii Article

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記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

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記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

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記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

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記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

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記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

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記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

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記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

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開催地：大阪大学  

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開催地：東京大学  

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開催地：東京大学  

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開催年月日： 2005年8月22日 - 2005年8月24日

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開催年月日： 2004年11月8日 - 2004年11月11日

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開催年月日： 2004年9月19日 - 2004年9月22日

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開催年月日： 2004年9月19日 - 2004年9月22日

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開催年月日： 2004年7月20日 - 2004年7月23日

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開催年月日： 2002年3月28日 - 2002年3月31日

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開催年月日： 2001年9月25日 - 2001年9月28日

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