The density of rational points on non-singular hypersurfaces, II

T.D. Browning, R. Heath Brown, J. Starr, Proceedings of the London Mathematical Society 93 (2006) 273–303.

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Abstract
For any integers d,n ≥2, let X ⊂ Pn be a non‐singular hypersurface of degree d that is defined over the rational numbers. The main result in this paper is a proof that the number of rational points on X which have height at most B is O(Bn − 1 + ɛ), for any ɛ > 0. The implied constant in this estimate depends at most upon d, ɛ and n. 2000 Mathematics Subject Classification 11D45 (primary), 11G35, 14G05 (secondary).
Publishing Year
Date Published
2006-09-01
Journal Title
Proceedings of the London Mathematical Society
Acknowledgement
EPSRC grant number GR/R93155/01
Volume
93
Issue
2
Page
273 - 303
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Browning TD, Heath Brown R, Starr J. The density of rational points on non-singular hypersurfaces, II. Proceedings of the London Mathematical Society. 2006;93(2):273-303. doi:https://doi.org/10.1112/S0024611506015784
Browning, T. D., Heath Brown, R., & Starr, J. (2006). The density of rational points on non-singular hypersurfaces, II. Proceedings of the London Mathematical Society, 93(2), 273–303. https://doi.org/10.1112/S0024611506015784
Browning, Timothy D, Roger Heath Brown, and Jason Starr. “The Density of Rational Points on Non-Singular Hypersurfaces, II.” Proceedings of the London Mathematical Society 93, no. 2 (2006): 273–303. https://doi.org/10.1112/S0024611506015784.
T. D. Browning, R. Heath Brown, and J. Starr, “The density of rational points on non-singular hypersurfaces, II,” Proceedings of the London Mathematical Society, vol. 93, no. 2, pp. 273–303, 2006.
Browning TD, Heath Brown R, Starr J. 2006. The density of rational points on non-singular hypersurfaces, II. Proceedings of the London Mathematical Society. 93(2), 273–303.
Browning, Timothy D., et al. “The Density of Rational Points on Non-Singular Hypersurfaces, II.” Proceedings of the London Mathematical Society, vol. 93, no. 2, John Wiley and Sons Ltd, 2006, pp. 273–303, doi:https://doi.org/10.1112/S0024611506015784.

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