Ukrainian Mathematical Journal

, Volume 56, Issue 10, pp 1712–1719 | Cite as

On Generalized Hardy Sums s5(h, k)

  • Y. Simsek


The aim of this paper is to study generalized Hardy sums s5(h, k). By using mediants and the adjacent difference of Farey fractions, we establish a relationship between s5(h, k) and Farey fractions. Using generalized Dedekind sums and a generalized periodic Bernoulli function, we define generalized Hardy sums s5,p(h,k). A relationship between s5,p(h, k) and the Hurwitz zeta function is established. By using the definitions of Lambert series and cotπz, we establish a relationship between s5(h,k) and Lambert series.


Zeta Function Hurwitz Zeta Function Bernoulli Function Farey Fraction Lambert Series 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Y. Simsek
    • 1
  1. 1.Mersin UniversityMersinTurkey

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