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Journal d'Analyse Mathématique

, Volume 137, Issue 1, pp 135–187 | Cite as

Uniform distribution of subpolynomial functions along primes and applications

  • Vitaly Bergelson
  • Grigori Kolesnik
  • Younghwan SonEmail author
Article
  • 13 Downloads

Abstract

Let H be a Hardy field (a field consisting of germs of real-valued functions at infinity that is closed under differentiation) and let fH be a subpolynomial function. Let P be the sequence of naturally ordered primes. We show that (f(n))n∈ℕ is uniformly distributed mod1 if and only if (f (p))p∈P is uniformly distributed mod 1. This result is then utilized to derive various ergodic and combinatorial statements which significantly generalize the results obtained in [BKMST].

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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  • Vitaly Bergelson
    • 1
  • Grigori Kolesnik
    • 2
  • Younghwan Son
    • 3
    Email author
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Department of MathematicsCalifornia State UniversityLos AngelesUSA
  3. 3.Department of MathematicsPOSTECHPohangSouth Korea

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