Reciprocity theorems for Dedekind sums and generalizations
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.
scientific article; zbMATH DE number 3533011
scientific article