Duke Mathematical Journal

The number of integral points on arcs and ovals

E. Bombieri and J. Pila

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J., Volume 59, Number 2 (1989), 337-357.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11P21: Lattice points in specified regions
Secondary: 11D99: None of the above, but in this section


Bombieri, E.; Pila, J. The number of integral points on arcs and ovals. Duke Math. J. 59 (1989), no. 2, 337--357. doi:10.1215/S0012-7094-89-05915-2. https://projecteuclid.org/euclid.dmj/1077308005

Export citation


  • [1] E. Bombieri, Le grand crible dans la théorie analytique des nombres, Astérisque (1987), no. 18, 103, Soc. Math. France, Paris.
  • [2] S. D. Cohen, The distribution of Galois groups and Hilbert's irreducibility theorem, Proc. London Math. Soc. (3) 43 (1981), no. 2, 227–250.
  • [3] D. Hilbert and A. Hurwitz, Über die diophantischen Gleichungen vom Geschlecht Null, Acta Mathematica 14 (1890-1891), 217–224.
  • [4] V. Jarnik, Über die Gitterpunkte auf konvexen Curven, Math. Z. 24 (1926), 500–518.
  • [5] D. J. Lewis and K. Mahler, On the representation of integers by binary forms, Acta Arith. 6 (1961), 333–363.
  • [6] C. Posse, Sur le terme complémentaire de la formule de M. Tchebychef donnant l'expression approchée d'une intégrale définie par d'autres prises entre les mêmes limites, Bull. Sci. Math. (2) 7 (1883), 214–224.
  • [7] P. Sarnak, Torsion points on varieties and homology of Abelian covers, manuscript, 1988.
  • [8] W. M. Schmidt, Integer Points on Curves and Surfaces, Monatsh. Math. 99 (1985), no. 1, 45–72.
  • [9] H. A. Schwarz, Verallgemeinerung eines analytischen Fundamentalsatzes, Annali di Mat. (2) 10 (1880), 129–136, rpt. Gesammelte Mathematische Abhandlungen, vol. 2, J. Springer, Berlin, 1890, pp. 296–302.
  • [10] H. P. F. Swinnerton-Dyer, The number of lattice points on a convex curve, J. Number Theory 6 (1974), 128–135.