Lattice points in d-dimensional spherical segments

被引：0

作者：

Martin Ortiz Ramirez

机构：

[1] University of Oxford,

来源：

Monatshefte für Mathematik | 2021年 / 194卷

关键词：

Discrete geometry; Lattice points on spheres; Diophantine approximation; 11P21; 11K60;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study lattice points in d-dimensional spheres, and count their number in thin spherical segments. We found an upper bound depending only on the radius of the sphere and opening angle of the segment. To obtain this bound we slice the segment by hyperplanes of rational direction, and then cover an arbitrary segment with one having rational direction. Diophantine approximation can be used to obtain the best rational direction possible.

引用

页码：167 / 179

页数：12

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