Reciprocity formulae for generalized Dedekind-Rademacher sums attached to three Dirichlet characters and related polynomial reciprocity formulae. (English) Zbl 07872245
In the very interesting paper under review, the author defines a three-character analogue of the generalized Dedekind-Rademacher sum introduced by Hall, Wilson, and Zagier and succeeds to establish its reciprocity formula which contains all of the reciprocity formulas in the literature for generalized Dedekind-Rademacher sums attached (and not attached) to Dirichlet characters as special cases. Furthermore, the author investigates some other interesting categories of sums, like certain cotangent sums which are associated to the Nyman-Beurling criterion for the Riemann Hypothesis.
The author also proves related polynomial reciprocity formulas which contain all of the polynomial reciprocity formulas in the literature as special cases, such as those given by Carlitz, Beck & Kohl, and the author of the paper under review.
Overall, the paper is well-written and constitutes a valuable contribution in the domain. I am sure it will be alluring to a broad spectrum of mathematicians working in Analytic Number Theory and beyond.
The author also proves related polynomial reciprocity formulas which contain all of the polynomial reciprocity formulas in the literature as special cases, such as those given by Carlitz, Beck & Kohl, and the author of the paper under review.
Overall, the paper is well-written and constitutes a valuable contribution in the domain. I am sure it will be alluring to a broad spectrum of mathematicians working in Analytic Number Theory and beyond.
Reviewer: Michael Th. Rassias (Vari)
Keywords:
character Dedekind sum; Dedekind-Rademacher sum; polynomial reciprocity formula; reciprocity formulaReferences:
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