@article { author = {Bourgain, J‎. ‎ and Rudnick, Z. and Sarnak, P.}, title = {Spatial statistics for lattice points on the sphere I‎: ‎Individual results}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {43}, number = {Issue 4 (Special Issue)}, pages = {361-386}, year = {2017}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, 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 = {Sums of three squares‎,‎spatial statistics‎,‎Ripley's functions‎}, url = {http://bims.iranjournals.ir/article_1169.html}, eprint = {http://bims.iranjournals.ir/article_1169_fba25bf5c43b78fe1eb1c4b9a4835c11.pdf} }