New arithmetical proof of the reciprocity law for Dedekind sums
Mouloud Goubi
TL;DR
This paper presents a new arithmetical proof of the reciprocity law for Dedekind sums, improving upon previous proofs by Rademacher and Whiteman, and offers insights into their properties for coprime integers.
Contribution
It introduces a novel arithmetical proof of the reciprocity law for Dedekind sums, enhancing understanding and simplifying the proof structure.
Findings
Provides a new proof method for Dedekind sum reciprocity law
Improves upon previous proofs by Rademacher and Whiteman
Offers clearer insights into the properties of Dedekind sums
Abstract
In this paper, for coprime numbers p and q we consider the well known Dedekind sums S(p,q) First, we give an improvement of the proof given by H. Rademacher and A. Whiteman, and we construct a new arithmetical proof for the reciprocity law
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Advanced Mathematical Theories