ON A GENERALIZATION OF A THEOREM OF POPOV

被引：0

作者：

Huang, Jing-Jing ^{[1
]}

Li, Huixi ^{[1
]}

机构：

[1] Univ Nevada, Dept Math & Stat, 1664 N Virginia St, Reno, NV 89557 USA

来源：

HOUSTON JOURNAL OF MATHEMATICS | 2020年 / 46卷 / 01期

关键词：

Lattice points; exponential sums; Erdos-Turan inequality; DIOPHANTINE APPROXIMATION; PLANAR CURVES; RATIONAL-POINTS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we obtain sharp estimates for the number of lattice points under and near the dilation of a general parabola, the former generalizing an old result of Popov. We apply Vaaler's lemma and the Erdos-Turan inequality to reduce the two underlying counting problems to mean values of a certain quadratic exponential sums, whose treatment is subject to classical analytic techniques.

引用

页码：27 / 38

页数：12

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