Equidistribution results for sequences of polynomials
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Colleges, School and Institutes
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.
|Journal||Journal of Number Theory|
|Early online date||14 Feb 2020|
|Publication status||E-pub ahead of print - 14 Feb 2020|
- Uniform distribution, Poissonian pair correlations