Integer chords and configurations of lattice points

被引：1

作者：

Huxley, M. N. ^{[1
]}

Plunkett, S. M. ^{[2
]}

机构：

[1] Cardiff Univ, Cardiff CF24 4AG, S Glam, Wales

[2] Univ Bristol, Bristol, Avon, England

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2016年 / 27卷 / 02期

关键词：

Lattice points; Configurations; Uniform distribution; Difference set; NUMBER;

D O I：

10.1016/j.indag.2015.12.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The area within a closed convex plane curve C may be estimated by enlarging C by a factor R, translating, counting the set J of integer points inside, and scaling back to the original size. This estimate is accurate when C is three times continuously differentiable in a certain sense. The set J is very sensitive to translations of the curve. We show that as R tends to infinity, the domains in which each set J occurs tend to uniform distribution modulo the integer lattice; this was only known for the special case of the circle. (C) 2016 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：534 / 545

页数：12

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