Spatial statistics for lattice points on the sphere I: Individual   results
  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. 
Jean Bourgain, Ze\'ev Rudnick and Peter Sarnak
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