### 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.

Original language | English (US) |
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Pages (from-to) | 361-386 |

Number of pages | 26 |

Journal | Bulletin of the Iranian Mathematical Society |

Volume | 43 |

Issue number | 4 Special Issue |

State | Published - Aug 2017 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

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

## Fingerprint Dive into the research topics of 'Spatial statistics for lattice points on the sphere I: Individual results'. Together they form a unique fingerprint.

## Cite this

Bourgain, J., Rudnick, Z., & Sarnak, P. (2017). Spatial statistics for lattice points on the sphere I: Individual results.

*Bulletin of the Iranian Mathematical Society*,*43*(4 Special Issue), 361-386.