q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series

Srivastava H., Kim T., ŞİMŞEK Y.

RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, vol.12, no.2, pp.241-268, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 2
  • Publication Date: 2005
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.241-268
  • Akdeniz University Affiliated: No


The main purpose of this paper is to present a systematic study of some families of multiple q-zeta functions and basic (or q-) L-series. In particular, by using the q-Volkenborn integration and uniform differentiation on Z(p), we construct p-adic q-zeta functions. These functions interpolate the q-Bernoulli numbers and polynomials. The values of p-adic q-zeta functions at negative integers are given explicitly. We also define new generating functions of q-Bernoulli numbers and polynomials. By using these functions, we prove the analytic continuation of some basic (or q-) L-series. These generating functions also interpolate Barnes' type Changhee q-Bernoulli numbers with attached Dirichlet character. By applying the Mellin transformation, we obtain relations between Barnes' type q-zeta function and new Barnes' type Changhee q-Bernoulli numbers. Furthermore, we construct the Dirichlet type Changhee basic (or q-) L-functions.