A uniform version of Jarník's theorem

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Algorithmique Arithmétique Expérimentale, CNRS UMR 9936, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France

strictly convex curve, integer points, Farey fractions

E. Bombieri and J. Pila, The number of integral points on arcs and ovals, Duke Math. J. 59 (1989), 337-357.
G. Grekos, Sur le nombre de points entiers d'une courbe convexe, Bull. Sci. Math. (2) 112 (1988), 235-254.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Clarendon Press, Oxford, 1979.
V. Jarník, Über die Gitterpunkte auf konvexen Kurven, Math. Z. 24 (1926), 500-518.
H. Niederreiter, The distribution of Farey points, Math. Ann. 201 (1973), 341-345.
J. Pila, Geometric postulation of a smooth function and the number of rational points, Duke Math. J. 63 (1991), 449-463.
W. M. Schmidt, Integer points on curves and surfaces, Monatsh. Math. 99 (1985), 45-72.
H. P. F. Swinnerton-Dyer, The number of lattice points on a convex curve, J. Number Theory 6 (1974), 128-135.
G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publication de l'Institut Élie Cartan, Nancy, 1990.
A. M. Vershik, The limit shape of convex lattice polygons and related topics, Functional Anal. Appl. 28 (1994), 13-20.