Approximation of rational numbers by Dedekind sums

Kurt Girstmair

Published 2013-10-03Version 1

Given a rational number $x$ and a bound $\varepsilon$, we exhibit $m,n$ such that $|x-12 s(m,n)|<\varepsilon$. Here $s(m,n)$ is the classical Dedekind sum and the parameters $m$ and $n$ are completely explicit in terms of $x$ and $\varepsilon$.