2023/10/26 by Yuan He, He, Yuan, Shi, Yong-Guo
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2310.17093
openalex publication_date 2023/10/26 · openalex created_date 2023/10/28 · openalex updated_date 2026/07/28
In this paper, we study the generalized Dedekind-Rademacher sums considered by Hall, Wilson and Zagier. We establish a formula for the products of two Bernoulli functions. The proof relies on Parseval's formula, Hurwitz's formula, and Lerch's functional equation. The result leads to reciprocity formulas for some generalizations of the classical Dedekind sums. In particular, it is shown that Carlitz's, Berndt's, Hall and Wilson's reciprocity theorems are deduced as special cases.