TY - JOUR
AU - Y. Simsek
PY - 2004/10/25
Y2 - 2024/05/28
TI - On Generalized Hardy Sums $s_5(h, k)$
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 56
IS - 10
SE - Short communications
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3856
AB - 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.
ER -