Reciprocity For Dedekind Sums via Conical Zeta Values

2025/12/23 by Yerko Torres-Nova, Torres-Nova, Yerko
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Combinatorial Mathematics

paper · doi:10.48550/arxiv.2512.20542

Abstract

We study reciprocity formulas for Dedekind sums associated with absolutely continuous functions, extending the classical Dedekind-Rademacher reciprocity formula. In particular, we treat the case of periodic Bernoulli functions. Our approach generalizes an integral method and uses Fourier analysis to show that the reciprocity for polynomial-type functions admits a geometric interpretation in terms of conical zeta values.

Citations

• On the geography of 3-folds via asymptotic behavior of invariants
• On the conical zeta values and the Dedekind zeta values for totally real fields
• Rational convex cones and cyclotomic multiple zeta values

Related

• Some reciprocity formulas for generalized Dedekind-Rademacher sums
• The Reciprocity Law for Dedekind Sums via the constant Ehrhart coefficient
• Reciprocity and the Kernel of Dedekind Sums
• Reciprocity formulas for certain generalized Hardy-Berndt sums
• On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions