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

Jean Bourgain, Zeév Rudnick, Peter Sarnak

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)361-386
Number of pages26
JournalBulletin of the Iranian Mathematical Society
Issue number4 Special Issue
StatePublished - Aug 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Ripley’s functions
  • Spatial statistics
  • Sums of three squares


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