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Rational points near planar curves and Diophantine approximation
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.Comment: 27 pages, corrected typos, to appear in Adv. Mat
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