The largest values of Dedekind sums

Abstract

Let [Formula: see text] denote the classical Dedekind sum, where [Formula: see text] is a positive integer and [Formula: see text], [Formula: see text]. For a given positive integer [Formula: see text], we describe a set of at most [Formula: see text] numbers [Formula: see text] for which [Formula: see text] may be [Formula: see text], provided that [Formula: see text] is sufficiently large. For the numbers [Formula: see text] not in this set, [Formula: see text].