A generalization of the Bombieri-Pila determinant method

Details A generalization of the Bombieri-Pila determinant method A generalization of the Bombieri-Pila determinant method

2009-05-27

arxiv.org/abs/0905.4443v2

Journal of Mathematical Sciences: Volume 171, Issue 6 (2010), Page 736

Mathematics

Number Theory

13 pages

Scientific paper

10.1007/s10958-010-0178-5

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.

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