q-Hardy-Berndt type sums associated with q-Genocchi type zeta and q-l-functions


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Simsek Y.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.71, no.12, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 71 Issue: 12
  • Publication Date: 2009
  • Doi Number: 10.1016/j.na.2008.11.014
  • Journal Name: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: q-Bernoulli numbers and polynomials, q-Genocchi zeta, q-l series, p-adic interpolation function, q-Dedekind type sums, q-Hardy-Berndt type sums, Q-EULER NUMBERS, Q-BERNOULLI NUMBERS, BASIC L-SERIES, THETA-FUNCTIONS, TWISTED EULER, POLYNOMIALS, DEDEKIND, EXTENSION
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this paper is to define new generating functions. By applying a derivative operator and the Mellin transformation to these generating functions, we define q-analogue of the Genocchi zeta function, q-analogue Hurwitz type Genocchi zeta function, and q-Genocchi type l-function. We define partial zeta function. By using this function, we construct p-adic interpolation functions which interpolate generalized q-Genocchi numbers at negative integers. We also define p-adic meromorphic functions on C(p). Furthermore, we construct new generating functions of q-Hardy-Berndt type sums and q-Hardy-Berndt type sums attached to Dirichlet character. We also give some new relations, related to these sums. (C) 2008 Elsevier Ltd. All rights reserved.