CHARACTER ANALOGUES OF CERTAIN HARDY–BERNDT SUMS
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Publication:5408836
DOI10.1142/S1793042113501200zbMath1309.11033arXiv1506.01867OpenAlexW2047004771MaRDI QIDQ5408836
Publication date: 11 April 2014
Published in: International Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1506.01867
Bernoulli and Euler numbers and polynomials (11B68) Dedekind eta function, Dedekind sums (11F20) Euler-Maclaurin formula in numerical analysis (65B15)
Related Items (7)
Transformation formulas of a character analogue of $\log \theta _{2}(z)$ ⋮ On generalized Eisenstein series and Ramanujan's formula for periodic zeta-functions ⋮ On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions ⋮ Character analogue of the Boole summation formula with applications ⋮ Reciprocity formulas for Hall-Wilson-Zagier type Hardy-Berndt sums ⋮ Higher-order character Dedekind sum ⋮ On reciprocity formula of character Dedekind sums and the integral of products of Bernoulli polynomials
Cites Work
- Degenerate and character Dedekind sums
- Generalized Cochrane sums and Cochrane-Hardy sums
- Three-term relations for Hardy sums
- Elementary proofs of Berndt's reciprocity laws
- Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications
- 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 \(s_3(h,k)\)
- A new generalization of Hardy-Berndt sums
- Analytic Properties of Arithmetic Sums Arising in the Theory of the Classical Theta-Functions
- The mean value of Hardy sums over short intervals
- A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity
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