Pair correlation and equidistribution on manifolds
Probability
2019-06-07 v2 Number Theory
Abstract
This study is motivated by a series of recent papers that show that, if a given deterministic sequence in the unit interval has a Poisson pair correlation function, then the sequence is uniformly distributed. Analogous results have been proved for point sequences on higher-dimensional tori. The purpose of this paper is to describe a simple statistical argument that explains this observation and furthermore permits a generalisation to bounded Euclidean domains as well as compact Riemannian manifolds.
Cite
@article{arxiv.1903.00670,
title = {Pair correlation and equidistribution on manifolds},
author = {Jens Marklof},
journal= {arXiv preprint arXiv:1903.00670},
year = {2019}
}
Comments
10 pages; to appear in Monatshefte fuer Mathematik