Rational points near planar curves and Diophantine approximation
Number Theory
2015-02-10 v2
Abstract
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 and Vaughan-Velani. Furthermore, we complete the Lebesgue theory of Diophantine approximation on weakly non-degenerate planar curves that was initially developed by Beresnevich-Zorin in the divergence case.
Cite
@article{arxiv.1403.7388,
title = {Rational points near planar curves and Diophantine approximation},
author = {Jing-Jing Huang},
journal= {arXiv preprint arXiv:1403.7388},
year = {2015}
}
Comments
27 pages, corrected typos, to appear in Adv. Math