On the mean value of the generalized Dedekind sum and certain generalized Hardy sums weighted by the Kloosterman sum

DOI10.1007/s11253-023-02234-2zbMath1528.11026MaRDI QIDQ6147982

Hamit Sever, Muhammet Cihat Dağlı

Publication date: 11 January 2024

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Kloosterman sumsgeneralized Hardy sums

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Gauss and Kloosterman sums; generalizations (11L05) Dedekind eta function, Dedekind sums (11F20)

Cites Work

• Some identities involving certain Hardy sum and Kloosterman sum
• The \(p\)-adic analytic Dedekind sums
• On generalized Dedekind sums involving quasi-periodic Euler functions
• On the mean values of Dedekind sums
• On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions
• An exact formula for an average of L-series
• Relations between theta-functions, Hardy sums, Eisenstein and Lambert series in the transformation formula of log \(\eta_{g,h}(z)\).
• Some arithmetic on the Hardy sums \(s_2(h,k)\) and \(s_3(h,k)\)
• Mean values of Dedekind sums
• On some identities involving certain Hardy sums and a Kloosterman sum
• On the identity involving certain Hardy sums and Kloosterman sums
• Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
• An identity involving Dedekind sums and generalized Kloosterman sums
• On Kloosterman's sum
• A hybrid mean value related to the Dedekind sums and Kloosterman sums
• A hybrid mean value related to the Dedekind sums and Kloosterman sums
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