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arXiv · 1309.4226

The number of Dedekind sums with equal fractional parts

Kurt Girstmair
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Abstract

In a previous it was shown that the Dedkind sums $12s(m,n)$ and $12s(x,n)$, $1\le m,x\le n$, $(m,n)=(x,n)=1$, are equal mod $\Z$ if, and only if, $(x-m)(xm-1)\equiv 0$ mod $n$. Here we determine the cardinality of numbers $x$ in the above range that satisfy this congruence for a given number $m$.

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Kurt Girstmair. 2013-10-22. The number of Dedekind sums with equal fractional parts. https://arxiv.org/abs/1309.4226

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