Multi-poly-Bernoulli numbers and related zeta functions

2015/03/07 by Masanobu Kaneko, Kaneko, Masanobu, Hirofumi Tsumura +1 · 2 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT) #Primary 11B68 #Secondary 11M32

paper · pdf · doi:10.48550/arxiv.1503.02156

openalex publication_date 2015/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ξ-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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• Contour Integration and Cyclotomic Apéry-Like Series Involving Generalized Binomial Coefficients
• Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types

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