66 citations · 211 across the 30 of their papers we have counts for
31 papers
Two formulas for certain double and multiple polylogarithms in two variables
Masanobu Kaneko, Hirofumi Tsumura
We give a weighted sum formula for the double polylogarithm in two variables, from which we can recover the classical weighted sum formulas for double zeta values, double -value…
Double Dirichlet series associated with arithmetic functions II
Kohji Matsumoto, Hirofumi Tsumura
This paper is a continuation of our previous work on double Dirichlet series associated with arithmetic functions such as the von Mangoldt function, the Möbius function, and so on.…
Multiple -values of level four, poly-Euler numbers, and related zeta functions
Masanobu Kaneko, Hirofumi Tsumura
We present several formulas for some specific multiple -values of conductor four. This grew out from the study of zeta functions of level four of Arakawa-Kaneko type. Closely re…
On poly-cosecant numbers
Masanobu Kaneko, Maneka Pallewatta, Hirofumi Tsumura
We introduce and study a `level two' generalization of the poly-Bernoulli numbers, which may also be regarded as a generalization of the cosecant numbers. We prove a recurrence rel…
On a variant of multiple zeta values of level two
Masanobu Kaneko, Hirofumi Tsumura
We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the `shuffle coun…
Zeta functions connecting multiple zeta values and poly-Bernoulli numbers
Masanobu Kaneko, Hirofumi Tsumura
We first review our previous works of Arakawa and the authors on two, closely related single-variable zeta functions. Their special values at positive and negative integer argument…
An overview and supplements to the theory of functional relations for zeta-functions of root systems
Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
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 sys…
Double Dirichlet series associated with arithmetic functions
Kohji Matsumoto, Akihiko Nawashiro, Hirofumi Tsumura
We consider double Dirichlet series associated with arithmetic functions such as the von Mangoldt function, the Möbius function, and so on. We show analytic continuations of them b…
Zeta-functions of root systems and Poincaré polynomials of Weyl groups
Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
We consider a certain linear combination of zeta-functions of root systems, where is a root system of rank and . Sh…
On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application
Masanobu Kaneko, Fumi Sakurai, Hirofumi Tsumura
We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating…
On Arakawa-Kaneko zeta-functions associated with and their functional relations
Yasushi Komori, Hirofumi Tsumura
We construct a certain class of Arakawa--Kaneko zeta-functions associated with , which includes the ordinary Arakawa--Kaneko zeta-function. We also define poly-Be…
Fundamentals of p-adic multiple L-functions and evaluation of their special values
Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto +1
We construct -adic multiple -functions in several variables, which are generalizations of the classical Kubota-Leopoldt -adic -functions, by using a specific -adic m…
Desingularization of complex multiple zeta-functions
Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto +1
We introduce the method of desingularization of multi-variable multiple zeta-functions (of the generalized Euler-Zagier type), under the motivation of finding suitable rigorous mea…
On multiple series of Eisenstein type
Henrik Bachmann, Hirofumi Tsumura
The aim of this paper is to study certain multiple series which can be regarded as multiple analogues of Eisenstein series. As a prior research, the second-named author considered…
Multi-poly-Bernoulli numbers and related zeta functions
Masanobu Kaneko, Hirofumi Tsumura
We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at non-positive integers and whose values at positive integers are linear combination…
Infinite series involving hyperbolic functions
Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
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 analo…
Lattice sums of hyperplane arrangements
Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
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…
Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type and evaluation of p-adic multiple L-functions at arbitrary integers
Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto +1
We study analytic properties of multiple zeta-functions of generalized Hurwitz-Lerch type. First, as a special type of them, we consider multiple zeta-functions of generalized Eule…
Desingularization of complex multiple zeta-functions, fundamentals of -adic multiple -functions, and evaluation of their special values
Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto +1
This paper deals with a multiple version of zeta- and L-functions both in the complex case and in the p-adic case: [I] Our motivation in the complex case is to find suitable rigoro…
On Witten multiple zeta-functions associated with semisimple Lie algebras V
Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
We study the values of the zeta-function of the root system of type at positive integer points. In our previous work we considered the case when all integers are even, but in…
A study on multiple zeta values from the viewpoint of zeta-functions of root systems
Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
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 -ple zeta-f…
Mean value theorems for the double zeta-function
Kohji Matsumoto, Hirofumi Tsumura
We prove asymptotic formulas for mean square values of the Euler double zeta-function , with respect to . Those formulas enable us to propose a double analogue o…
Functional relations for zeta-functions of weight lattices of Lie groups of type
Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
We study zeta-functions of weight lattices of compact connected semisimple Lie groups of type . Actually we consider zeta-functions of SU(4), SO(6) and PU(4), and give some fu…
Sum formulas for double polylogarithms with a shifting parameter and their derivatives
Kohji Matsumoto, Hirofumi Tsumura
We prove sum formulas for double polylogarithms of Hurwitz type, that is, involving a shifting parameter in the denominator. These formulas especially imply well-known sum form…