@article{Simsek_2004, title={On Generalized Hardy Sums $s_5(h, k)$}, volume={56}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3856}, abstractNote={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.}, number={10}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={SimsekY.}, year={2004}, month={Oct.}, pages={1434–1440} }