Lattice points in rotated convex domains

被引：6

作者：

Guo, Jingwei ^{[1
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2015年 / 31卷 / 02期

关键词：

Lattice points; convex domains; Fourier transform; Van der Corput's method; BODIES; DISCREPANCY; NUMBER;

D O I：

10.4171/RMI/839

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

If B subset of R-d (d >= 2) is a compact convex domain with a smooth boundary of finite type, we prove that for almost every rotation theta is an element of SO(d) the remainder of the lattice point problem, P-theta B (t) is of order O-theta(t(d-2+2/(d+1)-zeta d)) with a positive number zeta(d). Furthermore we extend the estimate of the above type, in the planar case, to general compact convex domains.

引用

页码：411 / 438

页数：28

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