Rational points near planar curves and Diophantine approximation

被引：20
|
作者：
Huang, Jing-Jing [1 ]
机构：
[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
来源：
ADVANCES IN MATHEMATICS | 2015年 / 274卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
Metric Diophantine approximation; Khintchine-Jarnik theorem; Rational points near curves;
D O I：
10.1016/j.aim.2015.01.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we establish asymptotic formulae with optimal errors for the number of rational points that are close to a planar curve, which unify and extend the results of Beresnevich-Dickinson-Velani [6] and Vaughan-Velani [22]. Furthermore, we complete the Lebesgue theory of Diophantine approximation on weakly non-degenerate planar curves that was initially developed by Beresnevich-Zorin [5] in the divergence case. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：490 / 515
页数：26
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