Fractional parts of Dedekind sums

Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec [Bilinear forms with Kloosterman fractions, Invent. Math. 128 (1997) 23-43] on double exponential sums with Kloosterman fractions, we establish a uniformity of distribution result for the fractional parts of Dedekind sums s(m, n) with m and n running over rather general sets. Our result extends earlier work of Myerson [Dedekind sums and uniform distribution, J. Number Theory 28 (1988) 233-239] and Vardi [A relation between Dedekind sums and Kloosterman sums, Duke Math. J. 55 (1987) 189-197]. Using different techniques, we also study the least denominator of the collection of Dedekind sums {s(m, n) : m ϵ (ℤ/nℤ)∗} on average for n ϵ [1, N].