Fractional parts of Dedekind sums

William D. Banks, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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].

Original languageEnglish
Pages (from-to)1137-1147
Number of pages11
JournalInternational Journal of Number Theory
Volume12
Issue number5
DOIs
Publication statusPublished - 1 Aug 2016
Externally publishedYes

Keywords

  • Dedekind sums
  • exponential sums
  • Kloosterman fractions
  • uniform distribution

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