Relations between theta-functions Hardy sums Eisenstein and Lambert series in the transformation formula of log eta(g,h)(z)

ŞİMŞEK Y.

JOURNAL OF NUMBER THEORY, vol.99, no.2, pp.338-360, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 99 Issue: 2
  • Publication Date: 2003
  • Doi Number: 10.1016/s0022-314x(02)00072-0
  • Journal Name: JOURNAL OF NUMBER THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.338-360
  • Keywords: generalized Dedekind eta-function and Dedekind sums, theta-function, Hardy sums, Bernoulli polynomials and (((x)) function Eisenstein series, Lambert series, Riemann zeta-function
  • Akdeniz University Affiliated: No

Abstract

In this paper. by using generalized logarithms of Dedekind eta-functions, generalized logarithms of theta-functions are obtained. Applying these functions, the relations between Hardy sums and Theta-functions are found. The special cases of these relations give Berndt's Theorems 6.1-8.1 (J. Reine Angew. Math. 303,304 (1978) 332) and explicit formulae of Hardy sums. Using derivative of logarithms of the Dedekind eta-function, relations between logarithm of the theta-functions and Eisenstein series are given, Applying connection between Lambert series and generalized Dedekind Sums. the relation between theta-functions and Lambert series are obtained. (C) 2002 Elsevier Science (USA). All rights reserved.