---
_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
orcid: 0000-0002-8314-0177
- 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.
Wiley-Blackwell. 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.
Wiley-Blackwell, 2006. 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. Wiley-Blackwell, 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: 2021-01-12T06:55:36Z
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'
...
---
_id: '216'
abstract:
- lang: eng
text: For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of
degree d. This article is concerned with the number Nz(B) of ℚ-rational points
on Z which have height at most B. For any ε > 0, we establish the estimate
NZ(B) = O d,ε,N(Bdim Z+ε), provided that d ≥ 6. As indicated, the implied constant
depends at most on d, ε, and N.
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: Per
full_name: Salberger, Per
last_name: Salberger
citation:
ama: Browning TD, Heath Brown R, Salberger P. Counting rational points on algebraic
varieties. Duke Mathematical Journal. 2006;132(3):545-578. doi:10.1215/S0012-7094-06-13236-2
apa: Browning, T. D., Heath Brown, R., & Salberger, P. (2006). Counting rational
points on algebraic varieties. Duke Mathematical Journal. Unknown. https://doi.org/10.1215/S0012-7094-06-13236-2
chicago: Browning, Timothy D, Roger Heath Brown, and Per Salberger. “Counting Rational
Points on Algebraic Varieties.” Duke Mathematical Journal. Unknown, 2006.
https://doi.org/10.1215/S0012-7094-06-13236-2.
ieee: T. D. Browning, R. Heath Brown, and P. Salberger, “Counting rational points
on algebraic varieties,” Duke Mathematical Journal, vol. 132, no. 3. Unknown,
pp. 545–578, 2006.
ista: Browning TD, Heath Brown R, Salberger P. 2006. Counting rational points on
algebraic varieties. Duke Mathematical Journal. 132(3), 545–578.
mla: Browning, Timothy D., et al. “Counting Rational Points on Algebraic Varieties.”
Duke Mathematical Journal, vol. 132, no. 3, Unknown, 2006, pp. 545–78,
doi:10.1215/S0012-7094-06-13236-2.
short: T.D. Browning, R. Heath Brown, P. Salberger, Duke Mathematical Journal 132
(2006) 545–578.
date_created: 2018-12-11T11:45:15Z
date_published: 2006-04-15T00:00:00Z
date_updated: 2021-01-12T06:55:41Z
day: '15'
doi: 10.1215/S0012-7094-06-13236-2
extern: 1
intvolume: ' 132'
issue: '3'
month: '04'
page: 545 - 578
publication: Duke Mathematical Journal
publication_status: published
publisher: Unknown
publist_id: '7696'
quality_controlled: 0
status: public
title: Counting rational points on algebraic varieties
type: journal_article
volume: 132
year: '2006'
...
---
_id: '218'
abstract:
- lang: eng
text: This paper is concerned with the average order of certain arithmetic functions,
as they range over the values taken by binary forms.
author:
- first_name: Régis
full_name: de la Bretèche, Régis
last_name: De La Bretèche
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: De La Bretèche R, Browning TD. Sums of arithmetic functions over values of
binary forms. Acta Arithmetica. 2006;125(3):291-304. doi:10.4064/aa125-3-6
apa: De La Bretèche, R., & Browning, T. D. (2006). Sums of arithmetic functions
over values of binary forms. Acta Arithmetica. Instytut Matematyczny. https://doi.org/10.4064/aa125-3-6
chicago: De La Bretèche, Régis, and Timothy D Browning. “Sums of Arithmetic Functions
over Values of Binary Forms.” Acta Arithmetica. Instytut Matematyczny,
2006. https://doi.org/10.4064/aa125-3-6.
ieee: R. De La Bretèche and T. D. Browning, “Sums of arithmetic functions over values
of binary forms,” Acta Arithmetica, vol. 125, no. 3. Instytut Matematyczny,
pp. 291–304, 2006.
ista: De La Bretèche R, Browning TD. 2006. Sums of arithmetic functions over values
of binary forms. Acta Arithmetica. 125(3), 291–304.
mla: De La Bretèche, Régis, and Timothy D. Browning. “Sums of Arithmetic Functions
over Values of Binary Forms.” Acta Arithmetica, vol. 125, no. 3, Instytut
Matematyczny, 2006, pp. 291–304, doi:10.4064/aa125-3-6.
short: R. De La Bretèche, T.D. Browning, Acta Arithmetica 125 (2006) 291–304.
date_created: 2018-12-11T11:45:16Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2021-01-12T06:55:49Z
day: '01'
doi: 10.4064/aa125-3-6
extern: 1
intvolume: ' 125'
issue: '3'
month: '01'
page: 291 - 304
publication: Acta Arithmetica
publication_status: published
publisher: Instytut Matematyczny
publist_id: '7694'
quality_controlled: 0
status: public
title: Sums of arithmetic functions over values of binary forms
type: journal_article
volume: 125
year: '2006'
...
---
_id: '2333'
alternative_title:
- Contemporary Mathematics
author:
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Jan
full_name: Solovej, Jan P
last_name: Solovej
citation:
ama: 'Lieb É, Seiringer R, Solovej J. Ground-state energy of a dilute Fermi gas.
In: Vol 412. American Mathematical Society; 2006:239-248. doi:10.1090/conm/412'
apa: Lieb, É., Seiringer, R., & Solovej, J. (2006). Ground-state energy of a
dilute Fermi gas (Vol. 412, pp. 239–248). Presented at the Differential Equations
and Mathematical Physics, American Mathematical Society. https://doi.org/10.1090/conm/412
chicago: Lieb, Élliott, Robert Seiringer, and Jan Solovej. “Ground-State Energy
of a Dilute Fermi Gas,” 412:239–48. American Mathematical Society, 2006. https://doi.org/10.1090/conm/412.
ieee: É. Lieb, R. Seiringer, and J. Solovej, “Ground-state energy of a dilute Fermi
gas,” presented at the Differential Equations and Mathematical Physics, 2006,
vol. 412, pp. 239–248.
ista: Lieb É, Seiringer R, Solovej J. 2006. Ground-state energy of a dilute Fermi
gas. Differential Equations and Mathematical Physics, Contemporary Mathematics,
vol. 412, 239–248.
mla: Lieb, Élliott, et al. Ground-State Energy of a Dilute Fermi Gas. Vol.
412, American Mathematical Society, 2006, pp. 239–48, doi:10.1090/conm/412.
short: É. Lieb, R. Seiringer, J. Solovej, in:, American Mathematical Society, 2006,
pp. 239–248.
conference:
name: Differential Equations and Mathematical Physics
date_created: 2018-12-11T11:57:03Z
date_published: 2006-01-01T00:00:00Z
date_updated: 2021-01-12T06:56:51Z
day: '01'
doi: 10.1090/conm/412
extern: 1
intvolume: ' 412'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0507049
month: '01'
oa: 1
page: 239 - 248
publication_status: published
publisher: American Mathematical Society
publist_id: '4593'
quality_controlled: 0
status: public
title: Ground-state energy of a dilute Fermi gas
type: conference
volume: 412
year: '2006'
...
---
_id: '2334'
author:
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Jakob
full_name: Yngvason, Jakob
last_name: Yngvason
citation:
ama: 'Seiringer R, Lieb É, Yngvason J. One-dimensional behavior of dilute, trapped
Bose gases in traps. In: Zambrini J, ed. World Scientific Publishing; 2006. doi:10.1007/s00220-003-0993-3'
apa: 'Seiringer, R., Lieb, É., & Yngvason, J. (2006). One-dimensional behavior
of dilute, trapped Bose gases in traps. In J. Zambrini (Ed.). Presented at the
ICMP: International Congress on Mathematical Physics, World Scientific Publishing.
https://doi.org/10.1007/s00220-003-0993-3'
chicago: Seiringer, Robert, Élliott Lieb, and Jakob Yngvason. “One-Dimensional Behavior
of Dilute, Trapped Bose Gases in Traps.” edited by Jean Zambrini. World Scientific
Publishing, 2006. https://doi.org/10.1007/s00220-003-0993-3.
ieee: 'R. Seiringer, É. Lieb, and J. Yngvason, “One-dimensional behavior of dilute,
trapped Bose gases in traps,” presented at the ICMP: International Congress on
Mathematical Physics, 2006.'
ista: 'Seiringer R, Lieb É, Yngvason J. 2006. One-dimensional behavior of dilute,
trapped Bose gases in traps. ICMP: International Congress on Mathematical Physics.'
mla: Seiringer, Robert, et al. One-Dimensional Behavior of Dilute, Trapped Bose
Gases in Traps. Edited by Jean Zambrini, World Scientific Publishing, 2006,
doi:10.1007/s00220-003-0993-3.
short: R. Seiringer, É. Lieb, J. Yngvason, in:, J. Zambrini (Ed.), World Scientific
Publishing, 2006.
conference:
name: 'ICMP: International Congress on Mathematical Physics'
date_created: 2018-12-11T11:57:03Z
date_published: 2006-03-07T00:00:00Z
date_updated: 2021-01-12T06:56:51Z
day: '07'
doi: 10.1007/s00220-003-0993-3
editor:
- first_name: Jean
full_name: Zambrini, Jean-Claude
last_name: Zambrini
extern: 1
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0305025
month: '03'
oa: 1
publication_status: published
publisher: World Scientific Publishing
publist_id: '4592'
quality_controlled: 0
status: public
title: One-dimensional behavior of dilute, trapped Bose gases in traps
type: conference
year: '2006'
...