Remark on a result of Bourgain on poissonian pair correlation

Gerhard Larcher

Remark on a result of Bourgain on poissonian pair correlation

Number Theory 2018-01-31 v2

Authors: Gerhard Larcher

Abstract

We show for a class of sequences $(a_n)_{n\geq 1}$ of distinct positive integers, that for no $\alpha$ the sequence $(\left\{a_n \alpha \right\})_{n \geq 1}$ does have Poissonian pair correlation. This class contains for example all strictly increasing integer sequences with positive upper density. This result motivates us to state a certain conjecture on Poissonian pair correlation which would be a significantly stronger version of a result of Jean Bourgain.

Keywords

poissonian pair correlation integer sequences upper density conjecture bourgain

Cite

@article{arxiv.1711.08663,
  title  = {Remark on a result of Bourgain on poissonian pair correlation},
  author = {Gerhard Larcher},
  journal= {arXiv preprint arXiv:1711.08663},
  year   = {2018}
}

Comments

2 figures, 13 pages

Related papers

View all related →