Том 69
№ 9

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

Simsek Y.

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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.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 10, pp 1712–1719.

Citation Example: Simsek Y. On Generalized Hardy Sums $s_5(h, k)$ // Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1434–1440.

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