# MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS

Masanobu Kaneko, Hirofumi Tsumura

8 被引用数 (Scopus)

## 抄録

We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at nonpositive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as the one to be paired up with the ξ-function defined by Arakawa and Kaneko. We show that both are closely related to the multiple zeta functions. Further we define multi-indexed poly-Bernoulli numbers, and generalize the duality formulas for poly-Bernoulli numbers by introducing more general zeta functions.

本文言語 英語 19-54 36 Nagoya Mathematical Journal 232 https://doi.org/10.1017/nmj.2017.16 出版済み - 12 1 2018

• 数学 (全般)

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