ON ANALYTIC PROPERTIES AND CHARACTER ANALOGS OF HARDY SUMS


Simsek Y.

TAIWANESE JOURNAL OF MATHEMATICS, vol.13, no.1, pp.253-268, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.11650/twjm/1500405282
  • Journal Name: TAIWANESE JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.253-268
  • Keywords: ((x))-function, Dedekind sum, Hardy sums, Farey fraction, Dirichlet character and L-function, Generalized Bernoulli numbers, THETA-FUNCTIONS, SERIES, EISENSTEIN
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this paper is to define Y(h, k) sum which is related to the Hardy's sums 85 (h, k). On the semi-group G, matrix operation of this sum is defined. Substituting mediants of Farey fractions into the matrix operation, Y(h, k) sum is generalized. By using contour integration, the reciprocity theorem of the Y(h, k) sum is proved. Moreover, by using L(1, chi) function and Gauss sums, generalized character analogs of the Hardy sums are found.