On the number of rational points on a strictly convex curve

Author： Petrov F.  

Publisher： Springer Publishing Company

ISSN： 0016-2663

Source： Functional Analysis and Its Applications, Vol.40, Iss.1, 2006-01, pp. : 24-33

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Abstract

Let γ be a bounded convex curve on the plane. Then #(γ ∩ (/n)2) = o(n 2/3). This strengthens the classical result due to Jarník [J] (the upper bound cn 2/3) and disproves the conjecture on the existence of a so-called universal Jarník curve.

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