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
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
收藏
页码:411 / 438
页数:28
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