AVERAGE NUMBER OF LATTICE POINTS IN A DISK

被引：6

作者：

Jayakar, Sujay ^{[1
]}

Strichartz, Robert S. ^{[2
]}

机构：

[1] 3633 19th St, San Francisco, CA 94110 USA

[2] Cornell Univ, Dept Math, Malott Hall, Ithaca, NY 14853 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2016年 / 15卷 / 01期

关键词：

Lattice points; Weyl asymptotics; Bessel function;

D O I：

10.3934/cpaa.2016.15.1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The difference between the number of lattice points in a disk of radius root t/2 pi and the area of the disk t/4 pi is equal to the error in the Weyl asymptotic estimate for the eigenvalue counting function of the Laplacian on the standard flat torus. We give a sharp asymptotic expression for the average value of the difference over the interval 0 <= t <= R. We obtain similar results for families of ellipses. We also obtain relations to the eigenvalue counting function for the Klein bottle and projective plane.

引用

页码：1 / 8

页数：8

共 11 条

[1] HARMONIC FUNCTIONS AND THE SPECTRUM OF THE LAPLACIAN ON THE SIERPINSKI CARPET [J].