On evaluation of the Dirichlet series at positive integers by \(q\)- calculation
type: Item
instance of: scholarly article
title: On evaluation of the Dirichlet series at positive integers by \(q\)- calculation
zbMATH Open document ID: 0807.11040
author: Hirofumi Tsumura
published in: Journal of Number Theory
publication date: 1994-09-28T00:00:00Z
review text: The author uses \(q\)-calculation to derive recursion formulas for values of the Riemann zeta function \(\zeta(s)\) at positive even integers. Analogous recursion formulas for \(\zeta(s)\) at positive odd integers involve series representations in terms of Euler numbers. The results are used to evaluate Dirichlet \(L\)-series at positive integers.
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 645306
zbMATH Keywords: values of Riemann zeta function at positive even integers
zbMATH Keywords: recursion formulas
zbMATH Keywords: positive odd integers
zbMATH Keywords: Dirichlet \(L\)-series at positive integers
reviewed by: Tom M. Apostol
MaRDI profile type: Publication
full work available at URL: jnth.1994.1074
OpenAlex ID: W2091998889
DOI: 10.1006/JNTH.1994.1074
description: scientific article; zbMATH DE number 645306