Journal of Mathematical Sciences

, Volume 171, Issue 6, pp 736–744 | Cite as

A generalization of the Bombieri–Pila determinant method


The so-called determinant method was developed by Bombieri and Pila in 1989 for counting integral points of bounded height on affine plane curves. In this paper, we give a generalization of that method to varieties of higher dimension, yielding a proof of Heath-Brown’s “Theorem 14” by real-analytic considerations alone. Bibliography: 11 titles.


High Dimension Rational Point Integral Point Projective Variety Plane Curf 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Chalmers University of Technology & University of GothenburgGothenburgSweden

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