A note on the Cochrane sum and its hybrid mean value formula.

DOI10.1016/J.JMAA.2003.09.056zbMath1046.11056OpenAlexW1968822906MaRDI QIDQ1419739

Huaning Liu, Wen Peng Zhang

Publication date: 26 January 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2003.09.056

zbMATH Keywords

asymptotic formulaCochrane sumsgeneral Kloosterman sums

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gauss and Kloosterman sums; generalizations (11L05) Dedekind eta function, Dedekind sums (11F20)

Related Items (14)

A hybrid mean value involving Cochrane sums and a new sum analogous to Kloosterman sums ⋮ Mean value on the difference between a quadratic residue and its inverse modulo \(p\) ⋮ General Kloosterman sums and the difference between an integer and its inverse modulo \(q\) ⋮ On the Gauss sums and generalized Bernoulli numbers ⋮ High-dimensional D. H. Lehmer problem over short intervals ⋮ Hybrid mean value on the difference between an integer and its inverse modulo \(q\) ⋮ Note on the mean value of higher-Kloosterman sums ⋮ Generalized Knopp identities for homogeneous Hardy sums and Cochrane-Hardy sums ⋮ On the hybrid mean value of Gauss sums and generalized Bernoulli numbers ⋮ On the mean value of \(\frac{L^{\prime}}{L}(1,\chi)\) ⋮ Generalized Cochrane sums and Cochrane-Hardy sums ⋮ Some applications of certain character sums ⋮ On Cochrane sums over short intervals ⋮ A mean value of Cochrane sum

Cites Work

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• An exact formula for an average of L-series
• On a Cochrane sum and its hybrid mean value formula. II
• Mean values of Dedekind sums
• A sum analogous to Dedekind sums and its hybrid mean value formula
• A note on the mean square value of the Dedekind sums
• On a Cochrane sum and its hybrid mean value formula.

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