Spatial statistics for lattice points on the sphere I: Individual results
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integerpointpointsresultssetsspatialspherestatistics
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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.
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Cited by 1 Pith paper
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Restriction of 3D arithmetic Laplace eigenfunctions to a plane
Expected nodal intersection length of random 3D toral eigenfunctions with a plane is proportional to area times wavenumber, with variance upper-bounded via lattice-point estimates on spheres.
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