Twisted p-adic (h, q)-L-functions

Simsek Y.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.59, no.6, pp.2097-2110, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 6
  • Publication Date: 2010
  • Doi Number: 10.1016/j.camwa.2009.12.015
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2097-2110
  • Keywords: q-Bernoulli numbers and polynomials, Twisted q-Bernoulli numbers and polynomials, q-zeta function, p-adic L-function, Twisted q-zeta function, Twisted q-L-function, q-Volkenborn integral, BERNOULLI NUMBERS, Q-ANALOG, ZETA-FUNCTIONS, L-SERIES, POLYNOMIALS, INTEGRALS, EULER, CONSTANTS, INTEGERS, BEHAVIOR
  • Akdeniz University Affiliated: Yes

Abstract

By using the q-Volkenborn integral on Z(p), in Simsek (2006) [33] and Simsek (2007) [34], generating functions for the (h, q)-Bernoulli polynomials and numbers were defined. By using these functions, we define a new twisted (h, q)-partial zeta function which interpolates the twisted (h, q)-Bernoulli polynomials and generalized twisted (h, q)Bernoulli numbers at negative integers. We give a relation between twisted (h, q)-partial zeta functions and the twisted (h, q)-two-variable L-function. We find the value of this function at s = 0. We also find the residue of this function at s = 1. We construct a p-adic twisted (h, q)-L-function which interpolates the twisted (h, q)-Bernoulli polynomials: