Reciprocity formulas for Hall-Wilson-Zagier type Hardy-Berndt sums

DOI10.1007/s10474-020-01101-xzbMath1474.11107arXiv2006.13323OpenAlexW3037723075MaRDI QIDQ2036601

Yanyan Li

Publication date: 29 June 2021

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.13323

zbMATH Keywords

Dedekind sumBernoulli and Euler polynomialHardy-Berndt sum

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Dedekind eta function, Dedekind sums (11F20) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Cites Work

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• Some identities involving certain Hardy sum and Kloosterman sum
• A cotangent sum related to zeros of the Estermann zeta function
• \(q\)-Hardy-Berndt type sums associated with \(q\)-Genocchi type zeta and \(q\)-\(l\)-functions
• On the theory of Dedekind sums.
• On certain sums generating the Dedekind sums and their reciprocity laws
• On the even power mean of a sum analogous to Dedekind sums
• Degenerate and character Dedekind sums
• A bias phenomenon on the behavior of Dedekind sums
• Generalized Cochrane sums and Cochrane-Hardy sums
• Three-term relations for Hardy sums
• Reciprocity theorems for Dedekind sums and generalizations
• On generalized Dedekind sums
• Toric varieties, lattice points and Dedekind sums
• Character analogues of Dedekind sums and transformations of analytic Eisenstein 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 \(s_3(h,k)\)
• Period functions and cotangent sums
• A new generalization of Hardy-Berndt sums
• Higher dimensional Dedekind sums
• Generalized Dedekind sums
• Transformation formulas of a character analogue of $\log \theta _{2}(z)$
• Generalized Dedekind sums and transformation formulae of certain Lambert series
• Theorems on generalized Dedekind sums
• Some theorems on generalized Dedekind sums
• A generalization of Rademacher's reciprocity law
• Bernoulli–Dedekind sums
• On reciprocity formulae for inhomogeneous and homogeneous Dedekind sums
• On a Category of Cotangent Sums Related to the Nyman-Beurling Criterion for the Riemann Hypothesis
• Analytic Properties of Arithmetic Sums Arising in the Theory of the Classical Theta-Functions
• p-ADIC q-HIGHER-ORDER HARDY-TYPE SUMS
• Computing the Continuous Discretely
• Arrangements of curves and algebraic surfaces
• Dedekind and Hardy sums
• Continued fractions and density results for Dedekind sums.
• Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
• Properties of certain integer-valued analogues of Dedekind sums
• Character analogue of the Boole summation formula with applications
• Reciprocity formulae for general Dedekind-Rademacher sums
• Generalized Knopp identities for homogeneous Hardy sums and Cochrane-Hardy sums
• Some remarks on certain generalized Dedekind sums
• CHARACTER ANALOGUES OF CERTAIN HARDY–BERNDT SUMS
• A Reciprocity Formula for a Cotangent Sum
• Generalizations of a cotangent sum associated to the Estermann zeta function

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