---
_id: '6620'
abstract:
- lang: eng
text: "This paper establishes an asymptotic formula with a power-saving error term
for the number of rational points of bounded height on the singular cubic surface
of ℙ3ℚ given by the following equation \U0001D4650(\U0001D46521+\U0001D46522)−\U0001D46533=0
in agreement with the Manin-Peyre conjectures.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Régis
full_name: De La Bretèche, Régis
last_name: De La Bretèche
- first_name: Kevin N
full_name: Destagnol, Kevin N
id: 44DDECBC-F248-11E8-B48F-1D18A9856A87
last_name: Destagnol
- first_name: Jianya
full_name: Liu, Jianya
last_name: Liu
- first_name: Jie
full_name: Wu, Jie
last_name: Wu
- first_name: Yongqiang
full_name: Zhao, Yongqiang
last_name: Zhao
citation:
ama: De La Bretèche R, Destagnol KN, Liu J, Wu J, Zhao Y. On a certain non-split
cubic surface. Science China Mathematics. 2019;62(12):2435–2446. doi:10.1007/s11425-018-9543-8
apa: De La Bretèche, R., Destagnol, K. N., Liu, J., Wu, J., & Zhao, Y. (2019).
On a certain non-split cubic surface. Science China Mathematics. Springer.
https://doi.org/10.1007/s11425-018-9543-8
chicago: De La Bretèche, Régis, Kevin N Destagnol, Jianya Liu, Jie Wu, and Yongqiang
Zhao. “On a Certain Non-Split Cubic Surface.” Science China Mathematics.
Springer, 2019. https://doi.org/10.1007/s11425-018-9543-8.
ieee: R. De La Bretèche, K. N. Destagnol, J. Liu, J. Wu, and Y. Zhao, “On a certain
non-split cubic surface,” Science China Mathematics, vol. 62, no. 12. Springer,
pp. 2435–2446, 2019.
ista: De La Bretèche R, Destagnol KN, Liu J, Wu J, Zhao Y. 2019. On a certain non-split
cubic surface. Science China Mathematics. 62(12), 2435–2446.
mla: De La Bretèche, Régis, et al. “On a Certain Non-Split Cubic Surface.” Science
China Mathematics, vol. 62, no. 12, Springer, 2019, pp. 2435–2446, doi:10.1007/s11425-018-9543-8.
short: R. De La Bretèche, K.N. Destagnol, J. Liu, J. Wu, Y. Zhao, Science China
Mathematics 62 (2019) 2435–2446.
date_created: 2019-07-07T21:59:25Z
date_published: 2019-12-01T00:00:00Z
date_updated: 2023-08-28T12:32:20Z
day: '01'
department:
- _id: TiBr
doi: 10.1007/s11425-018-9543-8
external_id:
arxiv:
- '1709.09476'
isi:
- '000509102200001'
intvolume: ' 62'
isi: 1
issue: '12'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1709.09476
month: '12'
oa: 1
oa_version: Preprint
page: 2435–2446
publication: Science China Mathematics
publication_identifier:
issn:
- '16747283'
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: On a certain non-split cubic surface
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 62
year: '2019'
...
---
_id: '6835'
abstract:
- lang: eng
text: We derive the Hasse principle and weak approximation for fibrations of certain
varieties in the spirit of work by Colliot-Thélène–Sansuc and Harpaz–Skorobogatov–Wittenberg.
Our varieties are defined through polynomials in many variables and part of our
work is devoted to establishing Schinzel's hypothesis for polynomials of this
kind. This last part is achieved by using arguments behind Birch's well-known
result regarding the Hasse principle for complete intersections with the notable
difference that we prove our result in 50% fewer variables than in the classical
Birch setting. We also study the problem of square-free values of an integer polynomial
with 66.6% fewer variables than in the Birch setting.
article_number: '102794'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Kevin N
full_name: Destagnol, Kevin N
id: 44DDECBC-F248-11E8-B48F-1D18A9856A87
last_name: Destagnol
- first_name: Efthymios
full_name: Sofos, Efthymios
last_name: Sofos
citation:
ama: Destagnol KN, Sofos E. Rational points and prime values of polynomials in moderately
many variables. Bulletin des Sciences Mathematiques. 2019;156(11). doi:10.1016/j.bulsci.2019.102794
apa: Destagnol, K. N., & Sofos, E. (2019). Rational points and prime values
of polynomials in moderately many variables. Bulletin Des Sciences Mathematiques.
Elsevier. https://doi.org/10.1016/j.bulsci.2019.102794
chicago: Destagnol, Kevin N, and Efthymios Sofos. “Rational Points and Prime Values
of Polynomials in Moderately Many Variables.” Bulletin Des Sciences Mathematiques.
Elsevier, 2019. https://doi.org/10.1016/j.bulsci.2019.102794.
ieee: K. N. Destagnol and E. Sofos, “Rational points and prime values of polynomials
in moderately many variables,” Bulletin des Sciences Mathematiques, vol.
156, no. 11. Elsevier, 2019.
ista: Destagnol KN, Sofos E. 2019. Rational points and prime values of polynomials
in moderately many variables. Bulletin des Sciences Mathematiques. 156(11), 102794.
mla: Destagnol, Kevin N., and Efthymios Sofos. “Rational Points and Prime Values
of Polynomials in Moderately Many Variables.” Bulletin Des Sciences Mathematiques,
vol. 156, no. 11, 102794, Elsevier, 2019, doi:10.1016/j.bulsci.2019.102794.
short: K.N. Destagnol, E. Sofos, Bulletin Des Sciences Mathematiques 156 (2019).
date_created: 2019-09-01T22:00:55Z
date_published: 2019-11-01T00:00:00Z
date_updated: 2023-08-29T07:18:02Z
day: '01'
department:
- _id: TiBr
doi: 10.1016/j.bulsci.2019.102794
external_id:
arxiv:
- '1801.03082'
isi:
- '000496342100002'
intvolume: ' 156'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1801.03082
month: '11'
oa: 1
oa_version: Preprint
publication: Bulletin des Sciences Mathematiques
publication_identifier:
issn:
- 0007-4497
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rational points and prime values of polynomials in moderately many variables
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 156
year: '2019'
...