On the duality formula for parametrized multiple series

Expressions of content-parametrized Schur multiple zeta-functions via the Giambelli formula

In this article, we consider the expressions for content-parametrized Schur multiple zeta-functions in terms of multiple zeta-functions of Euler-Zagier type and their star-variants, or in terms of modified zeta-functions of root systems. First of all, we focus on the Schur multiple zeta-function of hook type. And then, applying the Giambelli formula and induction argument, we obtain the expressions for general content-parametrized Schur multiple zeta-functions.

某些参数化多重泽塔值的循环和公式

Cyclic sum formula for certain parametrized multiple zeta values

本文针对Igarashi推广Ohno-Wakabayashi多重泽塔星值循环和公式后提出的三参数推广问题之一，给出了可能的解答。

Note on cyclic sum of certain parametrized multiple series

We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.

On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application

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 functions for these sums, from which the duality formula is apparent. Secondly we give an analytic proof of the duality from the viewpoint of our previous study of zeta-functions of Arakawa-Kaneko type. As an application, we give a formula that relates poly-Bernoulli numbers to the Genocchi numbers.

Duality formula and its generalization for Schur multiple zeta functions

In the study on multiple zeta values, the duality formula is one of the families of basic relations and plays an important role in the investigation of algebraic structure of the space spanned by all multiple zeta values along with the generalized duality formula (so called Ohno relation) obtained by the second author. In this article, we will discuss them for the Schur multiple zeta values which are the values at positive integers of the Schur multiple zeta function introduced by the first author, O. Phukswan and Y. Yamasaki.

Duality of Weighted Sum Formulas of Alternating Multiple $T$-Values

Recently, a new kind of multiple zeta value level two $T({\bf k})$ (which is called multiple $T$-values) was introduced and studied by Kaneko and Tsumura. In this paper, we define a kind of alternating version of multiple $T$-values, and study several duality formulas of weighted sum formulas about alternating multiple $T$-values by using the methods of iterated integral representations and series representations. Some special values of alternating multiple $T$-values can also be obtained.