MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS

Masanobu Kaneko, Hirofumi Tsumura

    Research output: Contribution to journalArticlepeer-review

    15 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

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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