On the distribution of lattice points on spheres and level surfaces of polynomials

被引：18

作者：

Magyar, Akos ^{[1
]}

机构：

[1] Univ Georgia, Dept Math, Boyd Grad Ctr, Athens, GA 30602 USA

来源：

JOURNAL OF NUMBER THEORY | 2007年 / 122卷 / 01期

基金：

美国国家科学基金会;

关键词：

discrepancy; lattice points; exponential sums;

D O I：

10.1016/j.jnt.2006.03.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The irregularities of distribution of lattice points on spheres and on level surfaces of polynomials are measured in terms of the discrepancy with respect to caps. It is found that the discrepancy depends on diophantine properties of the direction of the cap. If the direction of the cap is diophantine, in case of the spheres, close to optimal upper bounds are found. The estimates are based on a precise description of the Fourier transform of the set of lattice points on polynomial surfaces. (C) 2006 Elsevier Inc. All rights reserved.

引用

页码：69 / 83

页数：15

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