On the moduli of a Dedekind sum

Kurt Girstmair

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arXiv · 1808.02263

On the moduli of a Dedekind sum

Kurt Girstmair

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Abstract

Let $s(a,b)$ denote the classical Dedekind sum and $S(a,b)=12s(a,b)$. Let $k/q$, $q\in \Bbb N$, $k\in \Bbb Z$, $(k,q)=1$, be the value of $S(a,b)$. In a previous paper we showed that there are pairs $(a_r,b_r)$, $r\in\Bbb N$, such that $S(a_r,b_r)=k/q$ for all $r\in \Bbb N$, the $b_r$'s growing in $r$ exponentially. Here we exhibit such a sequence with $b_r$ a polynomial of degree $4$ in $r$.

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Kurt Girstmair. 2018-08-07. On the moduli of a Dedekind sum. https://arxiv.org/abs/1808.02263

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