Poisson spacing statistics for lattice points on circles

TL;DR

This paper demonstrates that for most radii, the spacing between lattice points on circles follows a Poisson distribution, revealing a statistical regularity in their arrangement.

Contribution

It establishes Poissonian spacing statistics for lattice points on circles along a density one subsequence of admissible radii.

Findings

Nearest neighbor spacings are Poissonian for most radii.

Spacing distribution converges to Poisson statistics.

Results hold along a density one subsequence.

Abstract

We show that along a density one subsequence of admissible radii, the nearest neighbor spacing between lattice points on circles is Poissonian.