On the values of a zeta function at non-positive integers
type: Item
instance of: scholarly article
title: On the values of a zeta function at non-positive integers
zbMATH Open document ID: 0733.11031
author: Chong-Hsio Fang
author: Minking Eie
published in: Pacific Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Let \({\tilde \zeta}\)(s)\(=\sum_{n_ 1\geq 1,n_ 2\geq 1,n_ 3\geq 0}(n_ 1n_ 2+(n_ 1+n_ 2)n_ 3)^{-s}\) for Re s\(>3/2\). The authors prove that \({\tilde \zeta}\)(s) can be meromorphically continued to the whole complex plane, and evaluate explicitly the values of this zeta-function at non-positive integers in terms of Bernoulli numbers. It turns out that \({\tilde \zeta}\)(-m)\(\in {\mathbb{Q}}\) for \(m\in {\mathbb{Z}}\), \(m\geq 0\).
reviewed by: B. Z. Moroz
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11E45
zbMATH DE Number: 4212158
zbMATH Keywords: Epstein zeta-function
zbMATH Keywords: analytic continuation
zbMATH Keywords: Bernoulli numbers
MaRDI profile type: Publication
full work available at URL: pjm.1990.145.201
OpenAlex ID: W2070139982
DOI: 10.2140/PJM.1990.145.201
description: scientific article; zbMATH DE number 4212158