Zeta functions connecting multiple zeta values and poly-Bernoulli numbers

Masanobu Kaneko; Hirofumi Tsumura

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arXiv · 1811.07736

Zeta functions connecting multiple zeta values and poly-Bernoulli numbers

Masanobu Kaneko·Hirofumi Tsumura

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Abstract

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 arguments are respectively multiple zeta values and poly-Bernoulli numbers. We then introduce, as a generalization of Sasaki's work, level 2 analogue of one of the two zeta functions and prove results analogous to those by Arakawa and the first named author.

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Masanobu Kaneko, Hirofumi Tsumura. 2018-11-19. Zeta functions connecting multiple zeta values and poly-Bernoulli numbers. https://arxiv.org/abs/1811.07736

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