\(q\)-Riemann zeta function
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.
scientific article; zbMATH DE number 2168633
scientific article