# Equidistribution results for sequences of polynomials

Research output: Contribution to journal › Article

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

Research output: Contribution to journal › Article

## Harvard

*Journal of Number Theory*. https://doi.org/10.1016/j.jnt.2020.01.003

## APA

*Journal of Number Theory*. https://doi.org/10.1016/j.jnt.2020.01.003

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## Bibtex

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## 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 -