---
OA_place: publisher
OA_type: hybrid
_id: '15337'
abstract:
- lang: eng
text: We prove the Manin–Peyre conjecture for the number of rational points of bounded
height outside of a thin subset on a family of Fano threefolds of bidegree (1,
2).
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).The authors are grateful to Florian Wilsch for useful comments. While
working on this paper the authors were supported by FWF grant P 32428.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Dante
full_name: Bonolis, Dante
id: 6A459894-5FDD-11E9-AF35-BB24E6697425
last_name: Bonolis
- 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: Zhizhong
full_name: Huang, Zhizhong
id: 21f1b52f-2fd1-11eb-a347-a4cdb9b18a51
last_name: Huang
citation:
ama: Bonolis D, Browning TD, Huang Z. Density of rational points on some quadric
bundle threefolds. Mathematische Annalen. 2024;390:4123-4207. doi:10.1007/s00208-024-02854-4
apa: Bonolis, D., Browning, T. D., & Huang, Z. (2024). Density of rational points
on some quadric bundle threefolds. Mathematische Annalen. Springer Nature.
https://doi.org/10.1007/s00208-024-02854-4
chicago: Bonolis, Dante, Timothy D Browning, and Zhizhong Huang. “Density of Rational
Points on Some Quadric Bundle Threefolds.” Mathematische Annalen. Springer
Nature, 2024. https://doi.org/10.1007/s00208-024-02854-4.
ieee: D. Bonolis, T. D. Browning, and Z. Huang, “Density of rational points on some
quadric bundle threefolds,” Mathematische Annalen, vol. 390. Springer Nature,
pp. 4123–4207, 2024.
ista: Bonolis D, Browning TD, Huang Z. 2024. Density of rational points on some
quadric bundle threefolds. Mathematische Annalen. 390, 4123–4207.
mla: Bonolis, Dante, et al. “Density of Rational Points on Some Quadric Bundle Threefolds.”
Mathematische Annalen, vol. 390, Springer Nature, 2024, pp. 4123–207, doi:10.1007/s00208-024-02854-4.
short: D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-04-21T22:00:53Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2026-07-29T09:56:42Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00208-024-02854-4
external_id:
arxiv:
- '2204.09322'
isi:
- '001204670500001'
file:
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checksum: 5dd51531deb1e4760c38c3c0c7d5aedc
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creator: dernst
date_created: 2025-01-09T09:08:14Z
date_updated: 2025-01-09T09:08:14Z
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file_name: 2024_MathAnnalen_Bonolis.pdf
file_size: 1019116
relation: main_file
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file_date_updated: 2025-01-09T09:08:14Z
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intvolume: ' 390'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 4123-4207
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: no
status: public
supplementarymaterial: no
title: Density of rational points on some quadric bundle threefolds
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 390
year: '2024'
...
---
_id: '10765'
abstract:
- lang: eng
text: We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski
open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate
integral quadratic form in n>3 variables and m is a non-zero integer. This gives
asymptotic formulas for the density of integral points taking coprime polynomial
values, which is a quantitative version of the arithmetic purity of strong approximation
property off infinity for affine quadrics.
acknowledgement: "We are grateful to Mikhail Borovoi, Zeev Rudnick and Olivier Wienberg
for their interest in our\r\nwork. We would like to address our gratitude to Ulrich
Derenthal for his generous support at Leibniz Universitat Hannover. We are in debt
to Tim Browning for an enlightening discussion and to the anonymous referees for
critical comments, which lead to overall improvements of various preliminary versions
of this paper. Part of this work was carried out and reported during a visit to
the University of Science and Technology of China. We thank Yongqi Liang for offering
warm hospitality. The first author was supported by a Humboldt-Forschungsstipendium.
The second author was supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft."
article_number: '108236'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yang
full_name: Cao, Yang
last_name: Cao
- first_name: Zhizhong
full_name: Huang, Zhizhong
id: 21f1b52f-2fd1-11eb-a347-a4cdb9b18a51
last_name: Huang
citation:
ama: Cao Y, Huang Z. Arithmetic purity of the Hardy-Littlewood property and geometric
sieve for affine quadrics. Advances in Mathematics. 2022;398(3). doi:10.1016/j.aim.2022.108236
apa: Cao, Y., & Huang, Z. (2022). Arithmetic purity of the Hardy-Littlewood
property and geometric sieve for affine quadrics. Advances in Mathematics.
Elsevier. https://doi.org/10.1016/j.aim.2022.108236
chicago: Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood
Property and Geometric Sieve for Affine Quadrics.” Advances in Mathematics.
Elsevier, 2022. https://doi.org/10.1016/j.aim.2022.108236.
ieee: Y. Cao and Z. Huang, “Arithmetic purity of the Hardy-Littlewood property and
geometric sieve for affine quadrics,” Advances in Mathematics, vol. 398,
no. 3. Elsevier, 2022.
ista: Cao Y, Huang Z. 2022. Arithmetic purity of the Hardy-Littlewood property and
geometric sieve for affine quadrics. Advances in Mathematics. 398(3), 108236.
mla: Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property
and Geometric Sieve for Affine Quadrics.” Advances in Mathematics, vol.
398, no. 3, 108236, Elsevier, 2022, doi:10.1016/j.aim.2022.108236.
short: Y. Cao, Z. Huang, Advances in Mathematics 398 (2022).
corr_author: '1'
das_tickbox: '0'
date_created: 2022-02-20T23:01:30Z
date_published: 2022-03-26T00:00:00Z
date_updated: 2026-08-19T13:00:41Z
day: '26'
department:
- _id: TiBr
doi: 10.1016/j.aim.2022.108236
external_id:
arxiv:
- '2003.07287'
isi:
- '000792517300014'
fulldoi: https://doi.org/10.1016/j.aim.2022.108236
intvolume: ' 398'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2003.07287
month: '03'
oa: 1
oa_version: Preprint
publication: Advances in Mathematics
publication_identifier:
eissn:
- 1090-2082
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Arithmetic purity of the Hardy-Littlewood property and geometric sieve for
affine quadrics
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 398
year: '2022'
...