---
_id: '213'
abstract:
- lang: eng
text: 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).
acknowledgement: EPSRC grant number GR/R93155/01
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Roger
full_name: Heath-Brown, Roger
last_name: Heath Brown
- first_name: Jason
full_name: Starr, Jason M
last_name: Starr
citation:
ama: 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
apa: 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. John Wiley and Sons Ltd. https://doi.org/10.1112/S0024611506015784
chicago: 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. John Wiley and Sons Ltd, 2006. https://doi.org/10.1112/S0024611506015784.
ieee: 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. John Wiley and Sons Ltd, pp. 273–303, 2006.
ista: 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.
mla: 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.
short: T.D. Browning, R. Heath Brown, J. Starr, Proceedings of the London Mathematical
Society 93 (2006) 273–303.
date_created: 2018-12-11T11:45:14Z
date_published: 2006-09-01T00:00:00Z
date_updated: 2021-01-12T06:55:29Z
day: '01'
doi: https://doi.org/10.1112/S0024611506015784
extern: 1
intvolume: ' 93'
issue: '2'
month: '09'
page: 273 - 303
publication: Proceedings of the London Mathematical Society
publication_status: published
publisher: John Wiley and Sons Ltd
publist_id: '7698'
quality_controlled: 0
status: public
title: The density of rational points on non-singular hypersurfaces, II
type: journal_article
volume: 93
year: '2006'
...