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

Jean Bourgain; Zeév Rudnick; Peter Sarnak

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

Jean Bourgain, Zeév Rudnick, Peter Sarnak

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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)
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

General Mathematics

Keywords

Ripley’s functions
Spatial statistics
Sums of three squares

Cite this

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title = "Spatial statistics for lattice points on the sphere I: Individual results",

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{\textquoteright}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.",

keywords = "Ripley{\textquoteright}s functions, Spatial statistics, Sums of three squares",

author = "Jean Bourgain and Ze{\'e}v Rudnick and Peter Sarnak",

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AU - Rudnick, Zeév

AU - Sarnak, Peter

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N2 - 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.

AB - 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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KW - Spatial statistics

KW - Sums of three squares

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M3 - Article

AN - SCOPUS:85030533953

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JO - Bulletin of the Iranian Mathematical Society

JF - Bulletin of the Iranian Mathematical Society

IS - 4 Special Issue

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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