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, cilt.12, sa.2, ss.241-268, 2005 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 2
  • Basım Tarihi: 2005
  • Dergi Adı: RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.241-268
  • Akdeniz Üniversitesi Adresli: Hayır

Özet

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.