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On Generalized Hardy Sums s 5(h, k)

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Abstract

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,p (h,k). A relationship between s 5,p (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.

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Authors and Affiliations

  1. Mersin University, Mersin, Turkey

    Y. Simsek

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  1. Y. Simsek
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1434–1440, October, 2004.

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Simsek, Y. On Generalized Hardy Sums s 5(h, k). Ukr Math J 56, 1712–1719 (2004). https://doi.org/10.1007/s11253-005-0146-2

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  • DOI: https://doi.org/10.1007/s11253-005-0146-2

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