---
_id: '6310'
abstract:
- lang: eng
text: An asymptotic formula is established for the number of rational points of
bounded anticanonical height which lie on a certain Zariskiopen subset of an arbitrary
smooth biquadratic hypersurface in sufficiently many variables. The proof uses
the Hardy–Littlewood circle method.
article_processing_charge: No
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: L.Q.
full_name: Hu, L.Q.
last_name: Hu
citation:
ama: Browning TD, Hu LQ. Counting rational points on biquadratic hypersurfaces.
Advances in Mathematics. 2019;349:920-940. doi:10.1016/j.aim.2019.04.031
apa: Browning, T. D., & Hu, L. Q. (2019). Counting rational points on biquadratic
hypersurfaces. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2019.04.031
chicago: Browning, Timothy D, and L.Q. Hu. “Counting Rational Points on Biquadratic
Hypersurfaces.” Advances in Mathematics. Elsevier, 2019. https://doi.org/10.1016/j.aim.2019.04.031.
ieee: T. D. Browning and L. Q. Hu, “Counting rational points on biquadratic hypersurfaces,”
Advances in Mathematics, vol. 349. Elsevier, pp. 920–940, 2019.
ista: Browning TD, Hu LQ. 2019. Counting rational points on biquadratic hypersurfaces.
Advances in Mathematics. 349, 920–940.
mla: Browning, Timothy D., and L. Q. Hu. “Counting Rational Points on Biquadratic
Hypersurfaces.” Advances in Mathematics, vol. 349, Elsevier, 2019, pp.
920–40, doi:10.1016/j.aim.2019.04.031.
short: T.D. Browning, L.Q. Hu, Advances in Mathematics 349 (2019) 920–940.
date_created: 2019-04-16T09:13:25Z
date_published: 2019-06-20T00:00:00Z
date_updated: 2023-08-25T10:11:55Z
day: '20'
ddc:
- '512'
department:
- _id: TiBr
doi: 10.1016/j.aim.2019.04.031
external_id:
arxiv:
- '1810.08426'
isi:
- '000468857300025'
file:
- access_level: open_access
checksum: a63594a3a91b4ba6e2a1b78b0720b3d0
content_type: application/pdf
creator: tbrownin
date_created: 2019-04-16T09:12:20Z
date_updated: 2020-07-14T12:47:27Z
file_id: '6311'
file_name: wliqun.pdf
file_size: 379158
relation: main_file
file_date_updated: 2020-07-14T12:47:27Z
has_accepted_license: '1'
intvolume: ' 349'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 920-940
publication: Advances in Mathematics
publication_identifier:
eissn:
- '10902082'
issn:
- '00018708'
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting rational points on biquadratic hypersurfaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 349
year: '2019'
...
---
_id: '1180'
abstract:
- lang: eng
text: In this article we define an algebraic vertex of a generalized polyhedron
and show that the set of algebraic vertices is the smallest set of points needed
to define the polyhedron. We prove that the indicator function of a generalized
polytope P is a linear combination of indicator functions of simplices whose vertices
are algebraic vertices of P. We also show that the indicator function of any generalized
polyhedron is a linear combination, with integer coefficients, of indicator functions
of cones with apices at algebraic vertices and line-cones. The concept of an algebraic
vertex is closely related to the Fourier–Laplace transform. We show that a point
v is an algebraic vertex of a generalized polyhedron P if and only if the tangent
cone of P, at v, has non-zero Fourier–Laplace transform.
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Imre
full_name: Bárány, Imre
last_name: Bárány
- first_name: Sinai
full_name: Robins, Sinai
last_name: Robins
citation:
ama: Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026
apa: Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex
polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026
chicago: Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of
Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.
ieee: A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,”
Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.
ista: Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 308, 627–644.
mla: Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances
in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.
short: A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.
date_created: 2018-12-11T11:50:34Z
date_published: 2017-02-21T00:00:00Z
date_updated: 2023-09-20T11:21:27Z
day: '21'
department:
- _id: HeEd
doi: 10.1016/j.aim.2016.12.026
ec_funded: 1
external_id:
isi:
- '000409292900015'
intvolume: ' 308'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1508.07594
month: '02'
oa: 1
oa_version: Submitted Version
page: 627 - 644
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Advances in Mathematics
publication_identifier:
issn:
- '00018708'
publication_status: published
publisher: Academic Press
publist_id: '6173'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Algebraic vertices of non-convex polyhedra
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 308
year: '2017'
...