A new generalization of Hardy-Berndt sums

DOI10.1007/s12044-013-0125-8zbMath1273.11037OpenAlexW2079480391MaRDI QIDQ2377076

Muhammet Cihat Dağlı, Mümün Can

Publication date: 27 June 2013

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-013-0125-8

zbMATH Keywords

Dedekind sumsBernoulli numbers and polynomialsHardy-Berndt sums

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Dedekind eta function, Dedekind sums (11F20)

Related Items (4)

Transformation formulas of a character analogue of $\log \theta _{2}(z)$ ⋮ Character analogue of the Boole summation formula with applications ⋮ CHARACTER ANALOGUES OF CERTAIN HARDY–BERNDT SUMS ⋮ Reciprocity formulas for Hall-Wilson-Zagier type Hardy-Berndt sums

Cites Work

• Unnamed Item
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• Elementary proofs of Berndt's reciprocity laws
• On generalized Dedekind sums
• Explicit formulas for degenerate Bernoulli numbers
• 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 \(s_3(h,k)\)
• Notes on degenerate numbers
• Generalized Dedekind sums
• Generalized Dedekind sums and transformation formulae of certain Lambert series
• Analytic Properties of Arithmetic Sums Arising in the Theory of the Classical Theta-Functions
• ON THE MEAN VALUES OF DEDEKIND SUMS AND HARDY SUMS
• Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
• Properties of certain integer-valued analogues of Dedekind sums
• The mean value of Hardy sums over short intervals

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