International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 12, Pages 599-605
doi:10.1155/S0161171204307180
q-Riemann zeta function
Institute of Science Education, Kongju National University, Kongju 314-701, South Korea
Received 19 July 2003
Copyright © 2004 Taekyun Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider the modified q-analogue of Riemann zeta function
which is defined by
ζq(s)=∑n=1∞(qn(s−1)/[n]s), 0<q<1, s∈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 nonarchimedean q-integration.