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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 377, Pages 63–77
(Mi znsl3815)
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This article is cited in 8 scientific papers (total in 8 papers)
A generalization of the Bombieri–Pila determinant method
O. Marmonab a Chalmers University of Technology, Goteborg, Sweden
b University of Gothenburg, Goteborg, Sweden
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. Bibl. 11 titles.
Key words and phrases:
rational points, integral points, determinant method.
Received: 11.05.2010
Citation:
O. Marmon, “A generalization of the Bombieri–Pila determinant method”, Studies in number theory. Part 10, Zap. Nauchn. Sem. POMI, 377, POMI, St. Petersburg, 2010, 63–77; J. Math. Sci. (N. Y.), 171:6 (2010), 736–744
Linking options:
https://www.mathnet.ru/eng/znsl3815 https://www.mathnet.ru/eng/znsl/v377/p63
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Abstract page: | 157 | Full-text PDF : | 50 | References: | 28 |
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