Counting rational points on hypersurfaces

T.D. Browning, R. Heath Brown, Journal Fur Die Reine Und Angewandte Mathematik (2005) 83–115.


Journal Article | Published
Author
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Abstract
For any n ≧ 2, let F ∈ ℤ [ x 1, … , xn ] be a form of degree d≧ 2, which produces a geometrically irreducible hypersurface in ℙn–1. This paper is concerned with the number N(F;B) of rational points on F = 0 which have height at most B. For any ε > 0 we establish the estimate N(F; B) = O(B n− 2+ ε ), whenever either n ≦ 5 or the hypersurface is not a union of lines. Here the implied constant depends at most upon d, n and ε.
Publishing Year
Date Published
2005-11-26
Journal Title
Journal fur die Reine und Angewandte Mathematik
Issue
584
Page
83 - 115
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Browning TD, Heath Brown R. Counting rational points on hypersurfaces. Journal fur die Reine und Angewandte Mathematik. 2005;(584):83-115. doi:https://doi.org/10.1515/crll.2005.2005.584.83
Browning, T. D., & Heath Brown, R. (2005). Counting rational points on hypersurfaces. Journal Fur Die Reine Und Angewandte Mathematik, (584), 83–115. https://doi.org/10.1515/crll.2005.2005.584.83
Browning, Timothy D, and Roger Heath Brown. “Counting Rational Points on Hypersurfaces.” Journal Fur Die Reine Und Angewandte Mathematik, no. 584 (2005): 83–115. https://doi.org/10.1515/crll.2005.2005.584.83.
T. D. Browning and R. Heath Brown, “Counting rational points on hypersurfaces,” Journal fur die Reine und Angewandte Mathematik, no. 584, pp. 83–115, 2005.
Browning TD, Heath Brown R. 2005. Counting rational points on hypersurfaces. Journal fur die Reine und Angewandte Mathematik. (584), 83–115.
Browning, Timothy D., and Roger Heath Brown. “Counting Rational Points on Hypersurfaces.” Journal Fur Die Reine Und Angewandte Mathematik, no. 584, Walter de Gruyter and Co , 2005, pp. 83–115, doi:https://doi.org/10.1515/crll.2005.2005.584.83.

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