On Generalized Hardy Sums s₅(h, k)
The aim of this paper is to study generalized Hardy sums s₅(h, k). By using mediants and the adjacent difference of Farey fractions, we establish a relationship between s₅(h, k) and Farey fractions. Using generalized Dedekind sums and a generalized periodic Bernoulli function, we define generalized...
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| Date: | 2004 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2004
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/164826 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Generalized Hardy Sums s₅(h, k) / Y. Simsek // Український математичний журнал. — 2004. — Т. 56, № 10. — С. 1434–1440. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | The aim of this paper is to study generalized Hardy sums s₅(h, k). By using mediants and the adjacent difference of Farey fractions, we establish a relationship between s₅(h, k) and Farey fractions. Using generalized Dedekind sums and a generalized periodic Bernoulli function, we define generalized Hardy sums s₅,p(h,k). A relationship between s₅,p(h, k) and the Hurwitz zeta function is established. By using the definitions of Lambert series and cotπz, we establish a relationship between s₅(h,k) and Lambert series. |
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