On a number of rational points on a convex curve

Fedor V. Petrov

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On a number of rational points on a convex curve

Fedor V. Petrov

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Abstract

Let $γ$ be a bounded convex curve on a plane. Then $\sharp (γ\cap (\Z/n)^2)=o(n^{2/3})$. It streghtens the classical result of Jarn\'ık (an upper estimate $O(n^{2/3})$) and disproves a conjecture of Vershik on existence of the so-called {\it universal Jarn\'ık curve}.

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BibTeX RIS

Fedor V. Petrov. 2005-03-15. On a number of rational points on a convex curve. https://arxiv.org/abs/math/0503304

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