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December 2021 Analytic continuation of multi-variable Arakawa-Kaneko zeta function for positive indices and its values at positive integers
Kunihiro Ito
Funct. Approx. Comment. Math. 65(2): 237-254 (December 2021). DOI: 10.7169/facm/1974

Abstract

We consider a multi-variable generalization of the zeta function defined by Arakawa and Kaneko. We establish its analytic continuation to an entire function,whence it follows that values at non-positive integersare expressed as multi-indexed poly-Bernoulli numbers of C-type. We also prove that its values at positive integers are in the space spanned by multiple zeta values.

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Kunihiro Ito. "Analytic continuation of multi-variable Arakawa-Kaneko zeta function for positive indices and its values at positive integers." Funct. Approx. Comment. Math. 65 (2) 237 - 254, December 2021. https://doi.org/10.7169/facm/1974

Information

Published: December 2021
First available in Project Euclid: 13 October 2021

Digital Object Identifier: 10.7169/facm/1974

Subjects:
Primary: 11M32
Secondary: 11B68

Keywords: Arakawa-Kaneko zeta function , multi-indexed poly-Bernoulli numbers , multiple zeta values

Rights: Copyright © 2021 Adam Mickiewicz University

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Vol.65 • No. 2 • December 2021
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