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arXiv · 1503.02156

Multi-poly-Bernoulli numbers and related zeta functions

Masanobu Kaneko·Hirofumi Tsumura
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Abstract

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 combinations of multiple zeta values. This function can be regarded as the one to be paired up with the $\xi$-function defined by Arakawa and the first-named author. 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.

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Masanobu Kaneko, Hirofumi Tsumura. 2015-03-07. Multi-poly-Bernoulli numbers and related zeta functions. https://arxiv.org/abs/1503.02156

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