q-Riemann zeta function

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.