Dedekind sums take each value infinitely many times

2017/05/24 by Kurt Girstmair, Girstmair, Kurt
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1705.08626

arxiv created 2017/05/24 · arxiv updated 2017/05/25

Abstract

For a∈ \Bbb Z and b∈\Bbb N, (a,b)=1, let s(a,b) denote the classical Dedekind sum. We show that Dedekind sums take this value infinitely many times in the following sense. There are pairs (a_i,b_i), i∈\Bbb N, with b_i tending to infinity as i grows, such that s(a_i,b_i)=s(a,b) for all i∈ \Bbb N.

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