Rational points near planar curves and Diophantine approximation

Jing-Jing Huang

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arXiv · 1403.7388

Rational points near planar curves and Diophantine approximation

Jing-Jing Huang

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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.

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Jing-Jing Huang. 2015-02-09. Rational points near planar curves and Diophantine approximation. https://arxiv.org/abs/1403.7388

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