English

A generalization of the Bombieri-Pila determinant method

Number Theory 2010-12-23 v2

Abstract

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.

Cite

@article{arxiv.0905.4443,
  title  = {A generalization of the Bombieri-Pila determinant method},
  author = {Oscar Marmon},
  journal= {arXiv preprint arXiv:0905.4443},
  year   = {2010}
}

Comments

13 pages

R2 v1 2026-06-21T13:06:41.183Z