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We study the spatial distribution of point sets on the sphere obtained fromthe representation of a large integer as a sum of three integer squares. Weexamine several statistics of these point sets, such as the electrostaticpotential, Ripley's function, the variance of the number of points in randomspherical caps, and the covering radius. Some of the results are conditional onthe Generalized Riemann Hypothesis.

Spatial statistics for lattice points on the sphere I: Individual results