Distribution of angles to lattice points seen from a fast moving observer

Jack Anderson; Florin P. Boca; Cristian Cobeli; Alexandru Zaharescu

doi:10.1007/s40993-024-00548-z

Distribution of angles to lattice points seen from a fast moving observer

Jack Anderson, Florin P. Boca, Cristian Cobeli, Alexandru Zaharescu

Mathematics

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

Abstract

We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles between rays from the observer towards the lattice points in the square. We prove the existence of the gap distribution as time tends to infinity and provide explicit formulas for the corresponding density function.

Original language	English (US)
Article number	62
Journal	Research in Number Theory
Volume	10
Issue number	3
DOIs	https://doi.org/10.1007/s40993-024-00548-z
State	Published - Sep 2024

Keywords

11B99
Exponential sums
Gap distribution of angles
Lattice points
Local spacing statistics
Primary 11P21
Secondary: 11K99

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1007/s40993-024-00548-z

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abstract = "We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles between rays from the observer towards the lattice points in the square. We prove the existence of the gap distribution as time tends to infinity and provide explicit formulas for the corresponding density function.",

keywords = "11B99, Exponential sums, Gap distribution of angles, Lattice points, Local spacing statistics, Primary 11P21, Secondary: 11K99",

author = "Jack Anderson and Boca, {Florin P.} and Cristian Cobeli and Alexandru Zaharescu",

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AU - Boca, Florin P.

AU - Cobeli, Cristian

AU - Zaharescu, Alexandru

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

PY - 2024/9

Y1 - 2024/9

N2 - We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles between rays from the observer towards the lattice points in the square. We prove the existence of the gap distribution as time tends to infinity and provide explicit formulas for the corresponding density function.

AB - We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles between rays from the observer towards the lattice points in the square. We prove the existence of the gap distribution as time tends to infinity and provide explicit formulas for the corresponding density function.

KW - 11B99

KW - Exponential sums

KW - Gap distribution of angles

KW - Lattice points

KW - Local spacing statistics

KW - Primary 11P21

KW - Secondary: 11K99

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ER -

Distribution of angles to lattice points seen from a fast moving observer

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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