Elementary proofs of Berndt's reciprocity laws

DOI10.2140/pjm.1982.98.17zbMath0479.10010OpenAlexW2089147967WikidataQ114845609 ScholiaQ114845609MaRDI QIDQ1161550

Tom M. Apostol, Thiennu H. Vu

Publication date: 1982

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1982.98.17

zbMATH Keywords

reciprocity lawsarithmetic sums analogous to Dedekind sumspolynomial reciprocity formula

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (8)

Relations between theta-functions, Hardy sums, Eisenstein and Lambert series in the transformation formula of log \(\eta_{g,h}(z)\). ⋮ Some special finite sums related to the three-term polynomial relations and their applications ⋮ Three-term relations for Hardy sums ⋮ Some arithmetic on the Hardy sums \(s_2(h,k)\) and \(s_3(h,k)\) ⋮ Transformation formulas of a character analogue of $\log \theta _{2}(z)$ ⋮ A new generalization of Hardy-Berndt sums ⋮ NON-COMMUTATIVE POLYNOMIAL RECIPROCITY FORMULAE ⋮ CHARACTER ANALOGUES OF CERTAIN HARDY–BERNDT SUMS

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