q-Riemann zeta function

Abstract

We consider the modifiedq-analogue of Riemann zeta function which is defined byζq(s)=∑n=1∞(qn(s−1)/[n]s),0<q<1,s∈ℂ. In this paper, we giveq-Bernoulli numbers which can be viewed as interpolation of the aboveq-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 ofq-Bernoulli numbers using nonarchimedeanq-integration.