Duke Mathematical Journal

Geometric postulation of a smooth function and the number of rational points

J. Pila

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Article information

Source
Duke Math. J., Volume 63, Number 2 (1991), 449-463.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077295930

Digital Object Identifier
doi:10.1215/S0012-7094-91-06320-9

Mathematical Reviews number (MathSciNet)
MR1115117

Zentralblatt MATH identifier
0763.11025

Subjects
Primary: 11J99: None of the above, but in this section

Citation

Pila, J. Geometric postulation of a smooth function and the number of rational points. Duke Math. J. 63 (1991), no. 2, 449--463. doi:10.1215/S0012-7094-91-06320-9. https://projecteuclid.org/euclid.dmj/1077295930


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References

  • [1] E. Bombieri and J. Pila, The number of integral points on arcs and ovals, Duke Math. J. 59 (1989), no. 2, 337–357.
  • [2] K. Mahler, Lectures on transcendental numbers, Springer-Verlag, Berlin, 1976.
  • [3]1 G. Pólya, On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1922), no. 4, 312–324.
  • [3]2 G. Pólya, Collected papers. Vol. III, Mathematicians of Our Time, vol. 21, MIT Press, Cambridge, MA, 1984.
  • [4] G. Pólya and G. Szegő, Problems and theorems in analysis. Vol. II, Springer-Verlag, New York, 1976.
  • [5] A. J. van der Poorten, Transcendental entire functions mapping every algebraic number field into itself, J. Austral. Math. Soc. 8 (1968), 192–193.
  • [6] W. M. Schmidt, Integer points on curves and surfaces, Monatsh. Math. 99 (1985), no. 1, 45–72.