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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 377, Pages 63–77 (Mi znsl3815)  
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
Full-text PDF (612 kB) Citations (8)
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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
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 171, Issue 6, Pages 736–744
DOI: https://doi.org/10.1007/s10958-010-0178-5
Bibliographic databases:
Document Type: Article
UDC: 512.752+511.515
Language: English
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
Citation in format AMSBIB
\Bibitem{Mar10}
\by O.~Marmon
\paper A generalization of the Bombieri--Pila determinant method
\inbook Studies in number theory. Part~10
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 377
\pages 63--77
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3815}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 171
\issue 6
\pages 736--744
\crossref{https://doi.org/10.1007/s10958-010-0178-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650037231}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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