On Generalized Hardy Sums $s_5(h, k)$

  • Y. Simsek


The aim of this paper is to study generalized Hardy sums $s_5(h, k)$. By using mediants and the adjacent difference of Farey fractions, we establish a relationship between $s_5(h, k)$ and Farey fractions. Using generalized Dedekind sums and a generalized periodic Bernoulli function, we define generalized Hardy sums $s_5(h, k)$. A relationship between $s_5(h, k)$ and the Hurwitz zeta function is established. By using the definitions of Lambert series and cotπz, we establish a relationship between $s_5(h, k)$ and Lambert series.
How to Cite
Simsek, Y. “On Generalized Hardy Sums $s_5(h, k)$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 10, Oct. 2004, pp. 1434–1440, https://umj.imath.kiev.ua/index.php/umj/article/view/3856.
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