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

2016/06/19 by Bourgain, Jean, Rudnick, Zeév, Sarnak, Peter
#11K36 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1606.05880

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.

Related

• Local statistics of lattice points on the sphere
• Average variance bounds for integer points on the sphere
• Random Point Sets on the Sphere --- Hole Radii, Covering, and Separation
• Uniform distribution on the sphere and caps
• A New Geometric Probability Technique for an N-dimensional Sphere and Its Applications to Physics