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Fractional parts of Dedekind sums

2014/11/07 by William D. Banks, Banks, William D., Igor E. Shparlinski +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1411.1820

Using recent results of S. Bettin and V. Chandee, arXiv 1502.00769, we have improved some of our results

arxiv created 2015/05/15 · arxiv updated 2015/05/19

Abstract

Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec~(1997) 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 (1988) and Vardi (1987). Using different techniques, we also study the least denominator of the collection of Dedekind sums \s(m,n):m∈(\mathbb Z/n \mathbb Z)^*\ on average for n∈[1,N].

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