Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43Issue 4 (Special Issue)20170830Spatial statistics for lattice points on the sphere I: Individual results3613861169ENJ. BourgainZ.RudnickP.SarnakJournal Article20171001We 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. http://bims.iranjournals.ir/article_1169_fba25bf5c43b78fe1eb1c4b9a4835c11.pdf