On the Number of Rational Points on a Strictly Convex Curve

Let $\gamma$ be a bounded convex curve on the plane. Then $\#(\gamma\cap(\mathbb{Z}/n)^2)=o(n^{2/3})$. This strengthens the classical result due to Jarník (the upper bound $cn^{2/3}$) and disproves the conjecture on the existence of a so-called universal Jarník curve.