On the equality of Dedekind sums

2021/02/12 by Kurt Girstmair, Girstmair, Kurt
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematics and Applications #math.NT #msc:11F20

paper · pdf · doi:10.48550/arxiv.2102.06374

arxiv created 2021/02/18 · arxiv updated 2021/02/19

Abstract

We show that deciding the equality of two Dedekind sums S(c,b), S(d,b) is equivalent to deciding whether a Dedekind sum defined by b, c, d takes a certain value. By means of this result we construct infinite sequences of pairwise equal Dedekind sums. Moreover, we prove a result that says how many Dedekind sums S(d,b), 1≤ d≤ b-1, may be equal to a given S(c,b) if b is a square-free number.

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