A uniform version of Jarník's theorem

• Autorzy: Alain Plagne
• Języki publikacji: EN

Słowa kluczowe

EN

strictly convex curve; integer points; Farey fractions

Kategorie tematyczne

• 11B57: Farey sequences; the sequences 1 k , 2 k , ⋯
• 11P21: Lattice points in specified regions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998-1999
• Tom: 87
• Numer: 3
• Strony: 255-267

Daty

wydano

1999

otrzymano

1998-01-21

poprawiono

1998-05-21

Twórcy

autor

Alain Plagne

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

Bibliografia

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