2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74503Let $γ$ 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}.8 pages, submitted to FAANumber TheoryMetric Geometry11H06text