International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 12, Pages 599-605

q-Riemann zeta function

Taekyun Kim

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.


We consider the modified q-analogue of Riemann zeta function which is defined by ζq(s)=n=1(qn(s1)/[n]s), 0<q<1, s. 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.