Equidistribution results for sequences of polynomials

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Equidistribution results for sequences of polynomials. / Baker, Simon.

In: Journal of Number Theory, 14.02.2020.

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@article{1e96dd91eb6a46ebaf1a8eec13fb76fe,
title = "Equidistribution results for sequences of polynomials",
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.",
keywords = "Uniform distribution, Poissonian pair correlations",
author = "Simon Baker",
year = "2020",
month = feb,
day = "14",
doi = "10.1016/j.jnt.2020.01.003",
language = "English",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Equidistribution results for sequences of polynomials

AU - Baker, Simon

PY - 2020/2/14

Y1 - 2020/2/14

N2 - 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.

AB - 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.

KW - Uniform distribution

KW - Poissonian pair correlations

U2 - 10.1016/j.jnt.2020.01.003

DO - 10.1016/j.jnt.2020.01.003

M3 - Article

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -