\(q\)-Riemann zeta function
type: Item
instance of: scholarly article
title: \(q\)-Riemann zeta function
zbMATH Open document ID: 1122.11082
DOI: 10.1155/S0161171204307180
author: Taekyun Kim
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/53490
review text: Summary: We consider the modified \(q\)-analogue of Riemann zeta function which is defined by \(\zeta_q(s)=\sum_{n=1}^{\infty}({q^{n(s-1)}}/{[n]^s})\), \(0<q<1\), \(s\in \mathbb{C}\). In this paper, we give \(q\)-Bernoulli numbers which can be viewed as interpolation of the above \(q\)-analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Also, we will treat some identities of \(q\)-Bernoulli numbers using non-archimedean \(q\)-integration.
Mathematics Subject Classification ID: 11S80
Mathematics Subject Classification ID: 05A30
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 33D15
zbMATH DE Number: 2168633
MaRDI profile type: Publication
OpenAlex ID: W2152112911
Recommended article: Q3577539
Recommended article: Q3764220
Recommended article: Q3710591
Recommended article: On \(q\)-analogues of Riemann's zeta function
Recommended article: \(q\)-analogue of Riemann's \(\zeta\)-function and \(q\)-Euler numbers
Recommended article: Q4074972
Recommended article: Riemann's zeta function
Recommended article: The Riemann zeta-function
Recommended article: Q4819889
description: scientific article; zbMATH DE number 2168633