2024 Asymptotic coefficientsof multiple zeta functions at the origin and generalized Gregory coefficients
Toshiki Matsusaka, Hideki Murahara, Tomokazu Onozuka
Funct. Approx. Comment. Math. Advance Publication 1-20 (2024). DOI: 10.7169/facm/240716-1-8

Abstract

Due to their singularities, multiple zeta functions behave sensitively at non-positive integer points. In this article, we focus on the asymptotic behavior at the origin $(0,\dots, 0)$ and unveil the generating series of the asymptotic coefficients as a generalization of the classical Gregory coefficients. This enables us to reveal the underlying symmetry of the asymptotic coefficients. Additionally, we extend the relationship between the asymptotic coefficients and the Gregory coefficients to include Hurwitz multiple zeta functions.

Citation

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Toshiki Matsusaka. Hideki Murahara. Tomokazu Onozuka. "Asymptotic coefficientsof multiple zeta functions at the origin and generalized Gregory coefficients." Funct. Approx. Comment. Math. Advance Publication 1 - 20, 2024. https://doi.org/10.7169/facm/240716-1-8

Information

Published: 2024
First available in Project Euclid: 16 December 2024

Digital Object Identifier: 10.7169/facm/240716-1-8

Subjects:
Primary: 11M32
Secondary: 11B68

Keywords: Gregory coefficients , multiple zeta functions

Rights: Copyright © 2024 Adam Mickiewicz University

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