Related papers: Explicit formulas of the relation between multiple…
Kaneko and Tsumura introduced the Arakawa-Kaneko type zeta function $\eta(-k_1,\ldots,-k_r;s_1,\ldots,s_r)$ for non-negative integers $k_1,\ldots,k_r$ and complex variables $s_1,\ldots,s_r$. Recently, Yamamoto showed that, by using the…
Recently, Kaneko and Tsumura introduced multiple $\widetilde{T}$-values, another kind of poly-Euler numbers and the related Arakawa-Kaneko type zeta function. It is shown that each of them satisfies similar formulas to those of multiple…
Many $\mathbb{Q}$-linear relations exist between multiple zeta values, the most interesting of which are various weighted sum formulas. In this paper, we generalized these to Euler sums and some other variants of multiple zeta values by…
In this paper, we introduce a new function, the multiple confluent hypergeometric functions, and establish a functional equation for the $r$-variable Euler--Zagier multiple zeta functions using it. In the case when $r=2$, this functional…
Kaneko and Tsumura introduced a new kind of multiple zeta functions $\eta(k_1,\ldots,k_r;s_1,\ldots,s_r)$. This is an analytic function of complex variables $s_1,\ldots,s_r$, while $k_1,\ldots,k_r$ are non-positive integer parameters. In…
In this paper, we establish some new identities of integrals involving multiple polylogarithm functions and their level two analogues in terms of Hurwitz-type multiple zeta (star) values. Using these identities, we provide new proofs of the…
We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.
We show the recurrence relations of the Euler-Zagier multiple zeta-function which describes the $r$-fold function with one variable specialized to a non-positive integer as a rational linear combination of $(r-1)$-fold functions, which…
In this paper, we construct certain analogues of the Arakawa-Kaneko zeta functions. We prove functional relations between these functions and the Mordell-Tornheim multiple zeta functions. Furthermore we give some formulas among…
In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple…
For these two decades, the Arakawa-Kaneko zeta function has been studied actively. Recently Kaneko and Tsumura constructed its variants from the viewpoint of poly-Bernoulli numbers. In this paper, we generalize their zeta functions of…
We present several formulas for some specific multiple $L$-values of conductor four. This grew out from the study of zeta functions of level four of Arakawa-Kaneko type. Closely related is a new version of multiple poly-Euler numbers and we…
T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an…
The sum formula is a well known relation in the field of the multiple zeta values. In this paper, we present its generalization for the Euler-Zagier multiple zeta function.
We give new closed and explicit formulas for "multiple zeta values" at non-positive integers of generalized Euler-Zagier multiple zeta-functions. We first prove these formulas for a small convenient class of these multiple zeta-functions…
Recently, the level two analogue of multiple polylogarithm function ${\rm A}(k_1,\ldots,k_r;z)$ and Arakawa-Kaneko zeta function $\psi(k_1,\ldots,k_r;s)$ were introduced by M. Kaneko and H. Tsumura, for $k_1,\ldots,k_r \in \mathbb{Z}_{\ge…
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…
One of the important research subjects in the study of multiple zeta functions is to clarify the linear relations and functional equations among them. The Schur multiple zeta functions are a generalization of the multiple zeta functions of…
The Kaneko--Zagier conjecture describes a correspondence between finite multiple zeta values and symmetric multiple zeta values. Its refined version has been established by Jarossay, Rosen and Ono--Seki--Yamamoto. In this paper, we…
We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler-Zagier type combinatorially. We first study their basic properties including a region of absolute convergence…