Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere
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.
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