Dedekind Sums and a Paper of G. H. Hardy
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Publication:4081306
DOI10.1112/jlms/s2-13.1.129zbMath0319.10006OpenAlexW1997838401MaRDI QIDQ4081306
Publication date: 1976
Published in: Journal of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1112/jlms/s2-13.1.129
Convergence and divergence of series and sequences (40A05) Arithmetic functions; related numbers; inversion formulas (11A25) Automorphic forms, one variable (11F12) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)
Related Items (23)
Relations between theta-functions, Hardy sums, Eisenstein and Lambert series in the transformation formula of log \(\eta_{g,h}(z)\). ⋮ Ramanujan’s Formula for ζ(2n + 1) ⋮ Three-term relations for Hardy sums ⋮ \(q\)-Dedekind type sums related to \(q\)-zeta function and basic \(L\)-series ⋮ On a secant Dirichlet series and Eichler integrals of Eisenstein series ⋮ Families of Twisted Bernoulli Numbers, Twisted Bernoulli Polynomials, and Their Applications ⋮ Unnamed Item ⋮ Cotangent zeta functions in function fields ⋮ On generalized Dedekind sums involving quasi-periodic Euler functions ⋮ Applications of the theory of modular forms to number theory ⋮ \(q\)-Hardy-Berndt type sums associated with \(q\)-Genocchi type zeta and \(q\)-\(l\)-functions ⋮ Extended higher Herglotz functions. I: Functional equations ⋮ Partial sums of the cotangent function ⋮ Generalized eta-functions and certain ray class invariants of real quadratic fields ⋮ Special functions related to Dedekind-type DC-sums and their applications ⋮ Elementary proof of the transformation formula for Lambert series involving generalized Dedekind sums ⋮ Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas ⋮ Secant zeta functions ⋮ Reciprocity theorems for Dedekind sums and generalizations ⋮ Special values of trigonometric Dirichlet series and Eichler integrals ⋮ Rationality of secant zeta values ⋮ NOTE ON q-DEDEKIND-TYPE SUMS RELATED TO q-EULER POLYNOMIALS ⋮ Explicit evaluations and reciprocity theorems for finite trigonometric sums
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