On Generalized Hardy Sums s_5(h, k) - Simsek, Y. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
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.