MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS

Masanobu Kaneko, Hirofumi Tsumura

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)19-54
Number of pages36
JournalNagoya Mathematical Journal
Volume232
DOIs
Publication statusPublished - Dec 1 2018

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Bernoulli numbers
Riemann zeta function
Multiple zeta Values
Integer
Linear Combination
Duality
Interpolate
Generalise

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS. / Kaneko, Masanobu; Tsumura, Hirofumi.

In: Nagoya Mathematical Journal, Vol. 232, 01.12.2018, p. 19-54.

Research output: Contribution to journalArticle

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