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

School of Mathematical Sciences

Tel Aviv University

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

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
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

Keywords

Ripley’s functions
Spatial statistics
Sums of three squares

All Science Journal Classification (ASJC) codes

General Mathematics

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.",

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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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SN - 1018-6301

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EP - 386

JO - BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY

JF - BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY

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ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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