q-Dedekind type sums related to q-zeta function and basic L-series

Simsek Y.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.318, no.1, pp.333-351, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 318 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1016/j.jmaa.2005.06.007
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.333-351
  • Keywords: Bernoulli functions, q-Riemann zeta, q-Hurwitz zeta function, q-Dirichlet L series, two-variable L-series, Dedekind sums, Q-ANALOG, TRANSFORMATION FORMULA, BERNOULLI NUMBERS, RECIPROCITY LAW
  • Akdeniz University Affiliated: Yes

Abstract

The main purpose of this paper is to define new generating functions. By applying the Mellin transformation formula. to these generating functions, we define q-analogue of Riemann zeta function, q-analogue Hurwitz zeta function, q-analogue Dirichlet L-function and two-variable q-L-function. In particular, by using these generating functions, we will construct new generating functions which produce q-Dedekind type sums and q-Dedekind type sums attached to Dirichlet character. We also give the relations between these sums and Dedekind sums. Furthermore, by using *-product which is given in this paper, we will give the relation between Dedekind sums and q-L function as well. (c) 2005 Elsevier Inc. All rights reserved.