Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere
Number Theory
2025-02-26 v1
Abstract
We consider rational points on the sphere and investigate their equidistribution in shrinking spherical caps. For the two-dimensional sphere, we leverage Hecke operators to obtain a significantly improved small-scale equidistribution bound, and discuss connections to the covering radius problem, intrinsic Diophantine approximation, and Linnik's conjecture on sums of two squares and a mini-square.
Cite
@article{arxiv.2502.17678,
title = {Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere},
author = {Claire Burrin and Matthias Gröbner},
journal= {arXiv preprint arXiv:2502.17678},
year = {2025}
}