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Ukrainian Mathematical Journal

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

On Generalized Hardy Sums s5(h, k)

  • Y. Simsek
Article

Abstract

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.

Keywords

Zeta Function Hurwitz Zeta Function Bernoulli Function Farey Fraction Lambert Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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