Equidistribution results for sequences of polynomials

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Abstract

Let (fn)n=1 be a sequence of polynomials and α >1. In this paper we study the distribution of the sequence (fn(α))n=1 modulo one. We give sufficient conditions for a sequence (fn)n=1to ensure that for Lebesgue almost every α >1the sequence (fn(α))n=1 has Poissonian pair correlations. In particular, this result implies that for Lebesgue almost every α >1, for any k≥2 the sequence (αnk)n=1 has Poissonian pair correlations.
Original languageEnglish
JournalJournal of Number Theory
Early online date14 Feb 2020
DOIs
Publication statusE-pub ahead of print - 14 Feb 2020

Keywords

  • Uniform distribution
  • Poissonian pair correlations

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