Spatial statistics for lattice points on the sphere I: Individual results
Number Theory
2016-08-02 v2 Classical Analysis and ODEs
Abstract
We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares. We examine several statistics of these point sets, such as the electrostatic potential, Ripley's function, the variance of the number of points in random spherical caps, and the covering radius. Some of the results are conditional on the Generalized Riemann Hypothesis.
Keywords
Cite
@article{arxiv.1606.05880,
title = {Spatial statistics for lattice points on the sphere I: Individual results},
author = {Jean Bourgain and Zeév Rudnick and Peter Sarnak},
journal= {arXiv preprint arXiv:1606.05880},
year = {2016}
}
Comments
Final version. To appear in the special issue of the Bulletin of the Iranian Mathematical Society (BIMS) in honor of Freydoon Shahidi's 70th birthday