Reciprocity theorems for Dedekind sums and generalizations
type: Item
instance of: scholarly article
title: Reciprocity theorems for Dedekind sums and generalizations
zbMATH Open document ID: 0342.10014
DOI: 10.1016/S0001-8708(77)80031-5
author: Bruce C. Berndt
published in: Advances in Mathematics
publication date: 1977-01-01T00:00:00Z
review text: This work is concerned with various types of Dedekind sums involving the first Bernoulli function only, i.e., \(((x))\) in the customary notation. All of the Dedekind sums examined here occur in the transformation formulae of functions akin to the logarithm of the Dedekind eta-function. Reciprocity and three-term relations are established for the sums. The methods are analytic, but transformation formulae are not used. Most of the theorems are not new. However, in some cases, the only previously known proofs utilized transformation formulas. Furthermore, the proofs given here are frequently simpler and shorter than other proofs.
Mathematics Subject Classification ID: 11F20
Mathematics Subject Classification ID: 11B68
zbMATH DE Number: 3533011
zbMATH Keywords: Dedekind sums
zbMATH Keywords: reciprocity relations
zbMATH Keywords: three-term relations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3533011