---
_id: '215'
abstract:
- lang: eng
text: For any n≥3, let F ∈ Z[X0,...,Xn ] be a form of degree d *≥5 that defines
a non-singular hypersurface X ⊂ Pn . The main result in this paper is a proof
of the fact that the number N (F ; B) of Q-rational points on X which have height
at most B satisfiesN (F ; B) = Od,ε,n (Bn −1+ε ), for any ε > 0. The implied
constant in this estimate depends at most upon d, ε and n. New estimates are also
obtained for the number of representations of a positive integer as the sum of
three dth powers, and for the paucity of integer solutions to equal sums of like
polynomials.*
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
- first_name: Roger
full_name: Heath-Brown, Roger
last_name: Heath Brown
citation:
ama: Browning TD, Heath Brown R. The density of rational points on non-singular
hypersurfaces, I. *Bulletin of the London Mathematical Society*. 2006;38(3):401-410.
doi:10.1112/S0024609305018412
apa: Browning, T. D., & Heath Brown, R. (2006). The density of rational points
on non-singular hypersurfaces, I. *Bulletin of the London Mathematical Society*,
*38*(3), 401–410. https://doi.org/10.1112/S0024609305018412
chicago: 'Browning, Timothy D, and Roger Heath Brown. “The Density of Rational Points
on Non-Singular Hypersurfaces, I.” *Bulletin of the London Mathematical Society*
38, no. 3 (2006): 401–10. https://doi.org/10.1112/S0024609305018412.'
ieee: T. D. Browning and R. Heath Brown, “The density of rational points on non-singular
hypersurfaces, I,” *Bulletin of the London Mathematical Society*, vol. 38,
no. 3, pp. 401–410, 2006.
ista: Browning TD, Heath Brown R. 2006. The density of rational points on non-singular
hypersurfaces, I. Bulletin of the London Mathematical Society. 38(3), 401–410.
mla: Browning, Timothy D., and Roger Heath Brown. “The Density of Rational Points
on Non-Singular Hypersurfaces, I.” *Bulletin of the London Mathematical Society*,
vol. 38, no. 3, Wiley-Blackwell, 2006, pp. 401–10, doi:10.1112/S0024609305018412.
short: T.D. Browning, R. Heath Brown, Bulletin of the London Mathematical Society
38 (2006) 401–410.
date_created: 2018-12-11T11:45:15Z
date_published: 2006-12-23T00:00:00Z
date_updated: 2019-04-26T07:22:09Z
day: '23'
doi: 10.1112/S0024609305018412
extern: 1
intvolume: ' 38'
issue: '3'
month: '12'
page: 401 - 410
publication: Bulletin of the London Mathematical Society
publication_status: published
publisher: Wiley-Blackwell
publist_id: '7697'
quality_controlled: 0
status: public
title: The density of rational points on non-singular hypersurfaces, I
type: journal_article
volume: 38
year: '2006'
...