---
_id: '10711'
abstract:
- lang: eng
text: In this paper, we investigate the distribution of the maximum of partial sums
of families of m -periodic complex-valued functions satisfying certain conditions.
We obtain precise uniform estimates for the distribution function of this maximum
in a near-optimal range. Our results apply to partial sums of Kloosterman sums
and other families of ℓ -adic trace functions, and are as strong as those obtained
by Bober, Goldmakher, Granville and Koukoulopoulos for character sums. In particular,
we improve on the recent work of the third author for Birch sums. However, unlike
character sums, we are able to construct families of m -periodic complex-valued
functions which satisfy our conditions, but for which the Pólya–Vinogradov inequality
is sharp.
acknowledgement: We would like to thank the anonymous referees for carefully reading
the paper and for their remarks and suggestions.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Pascal
full_name: Autissier, Pascal
last_name: Autissier
- first_name: Dante
full_name: Bonolis, Dante
id: 6A459894-5FDD-11E9-AF35-BB24E6697425
last_name: Bonolis
- first_name: Youness
full_name: Lamzouri, Youness
last_name: Lamzouri
citation:
ama: Autissier P, Bonolis D, Lamzouri Y. The distribution of the maximum of partial
sums of Kloosterman sums and other trace functions. Compositio Mathematica.
2021;157(7):1610-1651. doi:10.1112/s0010437x21007351
apa: Autissier, P., Bonolis, D., & Lamzouri, Y. (2021). The distribution of
the maximum of partial sums of Kloosterman sums and other trace functions. Compositio
Mathematica. Cambridge University Press. https://doi.org/10.1112/s0010437x21007351
chicago: Autissier, Pascal, Dante Bonolis, and Youness Lamzouri. “The Distribution
of the Maximum of Partial Sums of Kloosterman Sums and Other Trace Functions.”
Compositio Mathematica. Cambridge University Press, 2021. https://doi.org/10.1112/s0010437x21007351.
ieee: P. Autissier, D. Bonolis, and Y. Lamzouri, “The distribution of the maximum
of partial sums of Kloosterman sums and other trace functions,” Compositio
Mathematica, vol. 157, no. 7. Cambridge University Press, pp. 1610–1651, 2021.
ista: Autissier P, Bonolis D, Lamzouri Y. 2021. The distribution of the maximum
of partial sums of Kloosterman sums and other trace functions. Compositio Mathematica.
157(7), 1610–1651.
mla: Autissier, Pascal, et al. “The Distribution of the Maximum of Partial Sums
of Kloosterman Sums and Other Trace Functions.” Compositio Mathematica,
vol. 157, no. 7, Cambridge University Press, 2021, pp. 1610–51, doi:10.1112/s0010437x21007351.
short: P. Autissier, D. Bonolis, Y. Lamzouri, Compositio Mathematica 157 (2021)
1610–1651.
date_created: 2022-02-01T08:10:43Z
date_published: 2021-06-28T00:00:00Z
date_updated: 2023-08-17T06:59:16Z
day: '28'
department:
- _id: TiBr
doi: 10.1112/s0010437x21007351
external_id:
arxiv:
- '1909.03266'
isi:
- '000667289300001'
intvolume: ' 157'
isi: 1
issue: '7'
keyword:
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1909.03266
month: '06'
oa: 1
oa_version: Preprint
page: 1610-1651
publication: Compositio Mathematica
publication_identifier:
eissn:
- 1570-5846
issn:
- 0010-437X
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
status: public
title: The distribution of the maximum of partial sums of Kloosterman sums and other
trace functions
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 157
year: '2021'
...
---
_id: '8742'
abstract:
- lang: eng
text: We develop a version of Ekedahl’s geometric sieve for integral quadratic forms
of rank at least five. As one ranges over the zeros of such quadratic forms, we
use the sieve to compute the density of coprime values of polynomials, and furthermore,
to address a question about local solubility in families of varieties parameterised
by the zeros.
article_processing_charge: No
article_type: original
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: Roger
full_name: Heath-Brown, Roger
last_name: Heath-Brown
citation:
ama: Browning TD, Heath-Brown R. The geometric sieve for quadrics. Forum Mathematicum.
2021;33(1):147-165. doi:10.1515/forum-2020-0074
apa: Browning, T. D., & Heath-Brown, R. (2021). The geometric sieve for quadrics.
Forum Mathematicum. De Gruyter. https://doi.org/10.1515/forum-2020-0074
chicago: Browning, Timothy D, and Roger Heath-Brown. “The Geometric Sieve for Quadrics.”
Forum Mathematicum. De Gruyter, 2021. https://doi.org/10.1515/forum-2020-0074.
ieee: T. D. Browning and R. Heath-Brown, “The geometric sieve for quadrics,” Forum
Mathematicum, vol. 33, no. 1. De Gruyter, pp. 147–165, 2021.
ista: Browning TD, Heath-Brown R. 2021. The geometric sieve for quadrics. Forum
Mathematicum. 33(1), 147–165.
mla: Browning, Timothy D., and Roger Heath-Brown. “The Geometric Sieve for Quadrics.”
Forum Mathematicum, vol. 33, no. 1, De Gruyter, 2021, pp. 147–65, doi:10.1515/forum-2020-0074.
short: T.D. Browning, R. Heath-Brown, Forum Mathematicum 33 (2021) 147–165.
date_created: 2020-11-08T23:01:25Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-10-17T07:39:01Z
day: '01'
department:
- _id: TiBr
doi: 10.1515/forum-2020-0074
external_id:
arxiv:
- '2003.09593'
isi:
- '000604750900008'
intvolume: ' 33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2003.09593
month: '01'
oa: 1
oa_version: Preprint
page: 147-165
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Forum Mathematicum
publication_identifier:
eissn:
- 1435-5337
issn:
- 0933-7741
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
scopus_import: '1'
status: public
title: The geometric sieve for quadrics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2021'
...
---
_id: '9260'
abstract:
- lang: eng
text: We study the density of rational points on a higher-dimensional orbifold (Pn−1,Δ)
when Δ is a Q-divisor involving hyperplanes. This allows us to address a question
of Tanimoto about whether the set of rational points on such an orbifold constitutes
a thin set. Our approach relies on the Hardy–Littlewood circle method to first
study an asymptotic version of Waring’s problem for mixed powers. In doing so
we make crucial use of the recent resolution of the main conjecture in Vinogradov’s
mean value theorem, due to Bourgain–Demeter–Guth and Wooley.
acknowledgement: While working on this paper the authors were both supported by EPSRC
grant EP/P026710/1, and the second author received additional support from the NWO
Veni Grant 016.Veni.192.047. Thanks are due to Marta Pieropan, Arne Smeets and Sho
Tanimoto for useful conversations related to this topic, and to the anonymous referee
for numerous helpful suggestions.
article_processing_charge: No
article_type: original
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: Shuntaro
full_name: Yamagishi, Shuntaro
last_name: Yamagishi
citation:
ama: Browning TD, Yamagishi S. Arithmetic of higher-dimensional orbifolds and a
mixed Waring problem. Mathematische Zeitschrift. 2021;299:1071–1101. doi:10.1007/s00209-021-02695-w
apa: Browning, T. D., & Yamagishi, S. (2021). Arithmetic of higher-dimensional
orbifolds and a mixed Waring problem. Mathematische Zeitschrift. Springer
Nature. https://doi.org/10.1007/s00209-021-02695-w
chicago: Browning, Timothy D, and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional
Orbifolds and a Mixed Waring Problem.” Mathematische Zeitschrift. Springer
Nature, 2021. https://doi.org/10.1007/s00209-021-02695-w.
ieee: T. D. Browning and S. Yamagishi, “Arithmetic of higher-dimensional orbifolds
and a mixed Waring problem,” Mathematische Zeitschrift, vol. 299. Springer
Nature, pp. 1071–1101, 2021.
ista: Browning TD, Yamagishi S. 2021. Arithmetic of higher-dimensional orbifolds
and a mixed Waring problem. Mathematische Zeitschrift. 299, 1071–1101.
mla: Browning, Timothy D., and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional
Orbifolds and a Mixed Waring Problem.” Mathematische Zeitschrift, vol.
299, Springer Nature, 2021, pp. 1071–1101, doi:10.1007/s00209-021-02695-w.
short: T.D. Browning, S. Yamagishi, Mathematische Zeitschrift 299 (2021) 1071–1101.
date_created: 2021-03-21T23:01:21Z
date_published: 2021-03-05T00:00:00Z
date_updated: 2023-08-07T14:20:00Z
day: '05'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00209-021-02695-w
external_id:
isi:
- '000625573800002'
file:
- access_level: open_access
checksum: 8ed9f49568806894744096dbbca0ad7b
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T12:41:26Z
date_updated: 2021-03-22T12:41:26Z
file_id: '9279'
file_name: 2021_MathZeitschrift_Browning.pdf
file_size: 492685
relation: main_file
success: 1
file_date_updated: 2021-03-22T12:41:26Z
has_accepted_license: '1'
intvolume: ' 299'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 1071–1101
project:
- _id: 26A8D266-B435-11E9-9278-68D0E5697425
grant_number: EP-P026710-2
name: Between rational and integral points
publication: Mathematische Zeitschrift
publication_identifier:
eissn:
- 1432-1823
issn:
- 0025-5874
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Arithmetic of higher-dimensional orbifolds and a mixed Waring problem
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 299
year: '2021'
...
---
_id: '10415'
abstract:
- lang: eng
text: The Hardy–Littlewood circle method was invented over a century ago to study
integer solutions to special Diophantine equations, but it has since proven to
be one of the most successful all-purpose tools available to number theorists.
Not only is it capable of handling remarkably general systems of polynomial equations
defined over arbitrary global fields, but it can also shed light on the space
of rational curves that lie on algebraic varieties. This book, in which the arithmetic
of cubic polynomials takes centre stage, is aimed at bringing beginning graduate
students into contact with some of the many facets of the circle method, both
classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i
Balaguer Prize, a prestigious award for books of expository nature presenting
the latest developments in an active area of research in mathematics.
alternative_title:
- Progress in Mathematics
article_processing_charge: No
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: 'Browning TD. Cubic Forms and the Circle Method. Vol 343. Cham: Springer
Nature; 2021. doi:10.1007/978-3-030-86872-7'
apa: 'Browning, T. D. (2021). Cubic Forms and the Circle Method (Vol. 343).
Cham: Springer Nature. https://doi.org/10.1007/978-3-030-86872-7'
chicago: 'Browning, Timothy D. Cubic Forms and the Circle Method. Vol. 343.
Cham: Springer Nature, 2021. https://doi.org/10.1007/978-3-030-86872-7.'
ieee: 'T. D. Browning, Cubic Forms and the Circle Method, vol. 343. Cham:
Springer Nature, 2021.'
ista: 'Browning TD. 2021. Cubic Forms and the Circle Method, Cham: Springer Nature,
XIV, 166p.'
mla: Browning, Timothy D. Cubic Forms and the Circle Method. Vol. 343, Springer
Nature, 2021, doi:10.1007/978-3-030-86872-7.
short: T.D. Browning, Cubic Forms and the Circle Method, Springer Nature, Cham,
2021.
date_created: 2021-12-05T23:01:46Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2022-06-03T07:38:33Z
day: '01'
department:
- _id: TiBr
doi: 10.1007/978-3-030-86872-7
intvolume: ' 343'
language:
- iso: eng
month: '12'
oa_version: None
page: XIV, 166
place: Cham
publication_identifier:
eisbn:
- 978-3-030-86872-7
eissn:
- 2296-505X
isbn:
- 978-3-030-86871-0
issn:
- 0743-1643
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Cubic Forms and the Circle Method
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 343
year: '2021'
...
---
_id: '12076'
abstract:
- lang: eng
text: We find an asymptotic formula for the number of primitive vectors $(z_1,\ldots,z_4)\in
(\mathbb{Z}_{\neq 0})^4$ such that $z_1,\ldots, z_4$ are all squareful and bounded
by $B$, and $z_1+\cdots + z_4 = 0$. Our result agrees in the power of $B$ and
$\log B$ with the Campana-Manin conjecture of Pieropan, Smeets, Tanimoto and V\'{a}rilly-Alvarado.
article_number: '2104.06966'
article_processing_charge: No
arxiv: 1
author:
- first_name: Alec L
full_name: Shute, Alec L
id: 440EB050-F248-11E8-B48F-1D18A9856A87
last_name: Shute
orcid: 0000-0002-1812-2810
citation:
ama: Shute AL. Sums of four squareful numbers. arXiv. doi:10.48550/arXiv.2104.06966
apa: Shute, A. L. (n.d.). Sums of four squareful numbers. arXiv. https://doi.org/10.48550/arXiv.2104.06966
chicago: Shute, Alec L. “Sums of Four Squareful Numbers.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2104.06966.
ieee: A. L. Shute, “Sums of four squareful numbers,” arXiv. .
ista: Shute AL. Sums of four squareful numbers. arXiv, 2104.06966.
mla: Shute, Alec L. “Sums of Four Squareful Numbers.” ArXiv, 2104.06966,
doi:10.48550/arXiv.2104.06966.
short: A.L. Shute, ArXiv (n.d.).
date_created: 2022-09-09T10:42:51Z
date_published: 2021-04-15T00:00:00Z
date_updated: 2023-02-21T16:37:30Z
day: '15'
department:
- _id: TiBr
doi: 10.48550/arXiv.2104.06966
external_id:
arxiv:
- '2104.06966'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2104.06966
month: '04'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '12072'
relation: dissertation_contains
status: public
status: public
title: Sums of four squareful numbers
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '12077'
abstract:
- lang: eng
text: "We compare the Manin-type conjecture for Campana points recently formulated\r\nby
Pieropan, Smeets, Tanimoto and V\\'{a}rilly-Alvarado with an alternative\r\nprediction
of Browning and Van Valckenborgh in the special case of the orbifold\r\n$(\\mathbb{P}^1,D)$,
where $D =\\frac{1}{2}[0]+\\frac{1}{2}[1]+\\frac{1}{2}[\\infty]$. We find that
the two predicted leading constants do not agree, and we discuss whether thin
sets\r\ncould explain this discrepancy. Motivated by this, we provide a counterexample\r\nto
the Manin-type conjecture for Campana points, by considering orbifolds\r\ncorresponding
to squareful values of binary quadratic forms."
acknowledgement: The author would like to thank Damaris Schindler and Florian Wilsch
for their helpful comments on the heights and Tamagawa measures used in Section
3, together with Marta Pieropan, Sho Tanimoto and Sam Streeter for providing valuable
feedback on an earlier version of this paper, and Tim Browning for many useful comments
and discussions during the development of this work. The author is also grateful
to the anonymous referee for providing many valuable comments and suggestions that
improved the quality of the paper.
article_number: '2104.14946'
article_processing_charge: No
arxiv: 1
author:
- first_name: Alec L
full_name: Shute, Alec L
id: 440EB050-F248-11E8-B48F-1D18A9856A87
last_name: Shute
orcid: 0000-0002-1812-2810
citation:
ama: Shute AL. On the leading constant in the Manin-type conjecture for Campana
points. arXiv. doi:10.48550/arXiv.2104.14946
apa: Shute, A. L. (n.d.). On the leading constant in the Manin-type conjecture for
Campana points. arXiv. https://doi.org/10.48550/arXiv.2104.14946
chicago: Shute, Alec L. “On the Leading Constant in the Manin-Type Conjecture for
Campana Points.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2104.14946.
ieee: A. L. Shute, “On the leading constant in the Manin-type conjecture for Campana
points,” arXiv. .
ista: Shute AL. On the leading constant in the Manin-type conjecture for Campana
points. arXiv, 2104.14946.
mla: Shute, Alec L. “On the Leading Constant in the Manin-Type Conjecture for Campana
Points.” ArXiv, 2104.14946, doi:10.48550/arXiv.2104.14946.
short: A.L. Shute, ArXiv (n.d.).
date_created: 2022-09-09T10:43:17Z
date_published: 2021-04-30T00:00:00Z
date_updated: 2023-02-21T16:37:30Z
day: '30'
department:
- _id: TiBr
doi: 10.48550/arXiv.2104.14946
external_id:
arxiv:
- '2104.14946'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2104.14946
month: '04'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '12072'
relation: dissertation_contains
status: public
status: public
title: On the leading constant in the Manin-type conjecture for Campana points
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '177'
abstract:
- lang: eng
text: We develop a geometric version of the circle method and use it to compute
the compactly supported cohomology of the space of rational curves through a point
on a smooth affine hypersurface of sufficiently low degree.
article_processing_charge: No
article_type: original
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: Will
full_name: Sawin, Will
last_name: Sawin
citation:
ama: Browning TD, Sawin W. A geometric version of the circle method. Annals of
Mathematics. 2020;191(3):893-948. doi:10.4007/annals.2020.191.3.4
apa: Browning, T. D., & Sawin, W. (2020). A geometric version of the circle
method. Annals of Mathematics. Princeton University. https://doi.org/10.4007/annals.2020.191.3.4
chicago: Browning, Timothy D, and Will Sawin. “A Geometric Version of the Circle
Method.” Annals of Mathematics. Princeton University, 2020. https://doi.org/10.4007/annals.2020.191.3.4.
ieee: T. D. Browning and W. Sawin, “A geometric version of the circle method,” Annals
of Mathematics, vol. 191, no. 3. Princeton University, pp. 893–948, 2020.
ista: Browning TD, Sawin W. 2020. A geometric version of the circle method. Annals
of Mathematics. 191(3), 893–948.
mla: Browning, Timothy D., and Will Sawin. “A Geometric Version of the Circle Method.”
Annals of Mathematics, vol. 191, no. 3, Princeton University, 2020, pp.
893–948, doi:10.4007/annals.2020.191.3.4.
short: T.D. Browning, W. Sawin, Annals of Mathematics 191 (2020) 893–948.
date_created: 2018-12-11T11:45:02Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2023-08-17T07:12:37Z
day: '01'
department:
- _id: TiBr
doi: 10.4007/annals.2020.191.3.4
external_id:
arxiv:
- '1711.10451'
isi:
- '000526986300004'
intvolume: ' 191'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1711.10451
month: '05'
oa: 1
oa_version: Preprint
page: 893-948
publication: Annals of Mathematics
publication_status: published
publisher: Princeton University
publist_id: '7744'
quality_controlled: '1'
status: public
title: A geometric version of the circle method
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 191
year: '2020'
...
---
_id: '179'
abstract:
- lang: eng
text: An asymptotic formula is established for the number of rational points of
bounded anticanonical height which lie on a certain Zariski dense subset of the
biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified
Manin conjecture for this variety, in which the removal of a thin set of rational
points is allowed.
article_processing_charge: No
article_type: original
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: Roger
full_name: Heath Brown, Roger
last_name: Heath Brown
citation:
ama: Browning TD, Heath Brown R. Density of rational points on a quadric bundle
in ℙ3×ℙ3. Duke Mathematical Journal. 2020;169(16):3099-3165. doi:10.1215/00127094-2020-0031
apa: Browning, T. D., & Heath Brown, R. (2020). Density of rational points on
a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. Duke University Press.
https://doi.org/10.1215/00127094-2020-0031
chicago: Browning, Timothy D, and Roger Heath Brown. “Density of Rational Points
on a Quadric Bundle in ℙ3×ℙ3.” Duke Mathematical Journal. Duke University
Press, 2020. https://doi.org/10.1215/00127094-2020-0031.
ieee: T. D. Browning and R. Heath Brown, “Density of rational points on a quadric
bundle in ℙ3×ℙ3,” Duke Mathematical Journal, vol. 169, no. 16. Duke University
Press, pp. 3099–3165, 2020.
ista: Browning TD, Heath Brown R. 2020. Density of rational points on a quadric
bundle in ℙ3×ℙ3. Duke Mathematical Journal. 169(16), 3099–3165.
mla: Browning, Timothy D., and Roger Heath Brown. “Density of Rational Points on
a Quadric Bundle in ℙ3×ℙ3.” Duke Mathematical Journal, vol. 169, no. 16,
Duke University Press, 2020, pp. 3099–165, doi:10.1215/00127094-2020-0031.
short: T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 3099–3165.
date_created: 2018-12-11T11:45:02Z
date_published: 2020-09-10T00:00:00Z
date_updated: 2023-10-17T12:51:10Z
day: '10'
department:
- _id: TiBr
doi: 10.1215/00127094-2020-0031
external_id:
arxiv:
- '1805.10715'
isi:
- '000582676300002'
intvolume: ' 169'
isi: 1
issue: '16'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1805.10715
month: '09'
oa: 1
oa_version: Preprint
page: 3099-3165
publication: Duke Mathematical Journal
publication_identifier:
issn:
- 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
status: public
title: Density of rational points on a quadric bundle in ℙ3×ℙ3
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 169
year: '2020'
...
---
_id: '9007'
abstract:
- lang: eng
text: Motivated by a recent question of Peyre, we apply the Hardy–Littlewood circle
method to count “sufficiently free” rational points of bounded height on arbitrary
smooth projective hypersurfaces of low degree that are defined over the rationals.
article_processing_charge: No
article_type: original
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: Will
full_name: Sawin, Will
last_name: Sawin
citation:
ama: Browning TD, Sawin W. Free rational points on smooth hypersurfaces. Commentarii
Mathematici Helvetici. 2020;95(4):635-659. doi:10.4171/CMH/499
apa: Browning, T. D., & Sawin, W. (2020). Free rational points on smooth hypersurfaces.
Commentarii Mathematici Helvetici. European Mathematical Society. https://doi.org/10.4171/CMH/499
chicago: Browning, Timothy D, and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.”
Commentarii Mathematici Helvetici. European Mathematical Society, 2020.
https://doi.org/10.4171/CMH/499.
ieee: T. D. Browning and W. Sawin, “Free rational points on smooth hypersurfaces,”
Commentarii Mathematici Helvetici, vol. 95, no. 4. European Mathematical
Society, pp. 635–659, 2020.
ista: Browning TD, Sawin W. 2020. Free rational points on smooth hypersurfaces.
Commentarii Mathematici Helvetici. 95(4), 635–659.
mla: Browning, Timothy D., and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.”
Commentarii Mathematici Helvetici, vol. 95, no. 4, European Mathematical
Society, 2020, pp. 635–59, doi:10.4171/CMH/499.
short: T.D. Browning, W. Sawin, Commentarii Mathematici Helvetici 95 (2020) 635–659.
date_created: 2021-01-17T23:01:11Z
date_published: 2020-12-07T00:00:00Z
date_updated: 2023-08-24T11:11:36Z
day: '07'
department:
- _id: TiBr
doi: 10.4171/CMH/499
external_id:
arxiv:
- '1906.08463'
isi:
- '000596833300001'
intvolume: ' 95'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1906.08463
month: '12'
oa: 1
oa_version: Preprint
page: 635-659
publication: Commentarii Mathematici Helvetici
publication_identifier:
eissn:
- '14208946'
issn:
- '00102571'
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Free rational points on smooth hypersurfaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 95
year: '2020'
...
---
_id: '10874'
abstract:
- lang: eng
text: In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler,
and Zykin, which allows us to connect invariants of binary octics to Siegel modular
forms of genus 3. We use this connection to show that certain modular functions,
when restricted to the hyperelliptic locus, assume values whose denominators are
products of powers of primes of bad reduction for the associated hyperelliptic
curves. We illustrate our theorem with explicit computations. This work is motivated
by the study of the values of these modular functions at CM points of the Siegel
upper half-space, which, if their denominators are known, can be used to effectively
compute models of (hyperelliptic, in our case) curves with CM.
acknowledgement: "The authors would like to thank the Lorentz Center in Leiden for
hosting the Women in Numbers Europe 2 workshop and providing a productive and enjoyable
environment for our initial work on this project. We are grateful to the organizers
of WIN-E2, Irene Bouw, Rachel Newton and Ekin Ozman, for making this conference
and this collaboration possible. We\r\nthank Irene Bouw and Christophe Ritzenhaler
for helpful discussions. Ionica acknowledges support from the Thomas Jefferson Fund
of the Embassy of France in the United States and the FACE Foundation. Most of Kılıçer’s
work was carried out during her stay in Universiteit Leiden and Carl von Ossietzky
Universität Oldenburg. Massierer was supported by the Australian Research Council
(DP150101689). Vincent is supported by the National Science Foundation under Grant
No. DMS-1802323 and by the Thomas Jefferson Fund of the Embassy of France in the
United States and the FACE Foundation. "
article_number: '9'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sorina
full_name: Ionica, Sorina
last_name: Ionica
- first_name: Pınar
full_name: Kılıçer, Pınar
last_name: Kılıçer
- first_name: Kristin
full_name: Lauter, Kristin
last_name: Lauter
- first_name: Elisa
full_name: Lorenzo García, Elisa
last_name: Lorenzo García
- first_name: Maria-Adelina
full_name: Manzateanu, Maria-Adelina
id: be8d652e-a908-11ec-82a4-e2867729459c
last_name: Manzateanu
- first_name: Maike
full_name: Massierer, Maike
last_name: Massierer
- first_name: Christelle
full_name: Vincent, Christelle
last_name: Vincent
citation:
ama: Ionica S, Kılıçer P, Lauter K, et al. Modular invariants for genus 3 hyperelliptic
curves. Research in Number Theory. 2019;5. doi:10.1007/s40993-018-0146-6
apa: Ionica, S., Kılıçer, P., Lauter, K., Lorenzo García, E., Manzateanu, M.-A.,
Massierer, M., & Vincent, C. (2019). Modular invariants for genus 3 hyperelliptic
curves. Research in Number Theory. Springer Nature. https://doi.org/10.1007/s40993-018-0146-6
chicago: Ionica, Sorina, Pınar Kılıçer, Kristin Lauter, Elisa Lorenzo García, Maria-Adelina
Manzateanu, Maike Massierer, and Christelle Vincent. “Modular Invariants for Genus
3 Hyperelliptic Curves.” Research in Number Theory. Springer Nature, 2019.
https://doi.org/10.1007/s40993-018-0146-6.
ieee: S. Ionica et al., “Modular invariants for genus 3 hyperelliptic curves,”
Research in Number Theory, vol. 5. Springer Nature, 2019.
ista: Ionica S, Kılıçer P, Lauter K, Lorenzo García E, Manzateanu M-A, Massierer
M, Vincent C. 2019. Modular invariants for genus 3 hyperelliptic curves. Research
in Number Theory. 5, 9.
mla: Ionica, Sorina, et al. “Modular Invariants for Genus 3 Hyperelliptic Curves.”
Research in Number Theory, vol. 5, 9, Springer Nature, 2019, doi:10.1007/s40993-018-0146-6.
short: S. Ionica, P. Kılıçer, K. Lauter, E. Lorenzo García, M.-A. Manzateanu, M.
Massierer, C. Vincent, Research in Number Theory 5 (2019).
date_created: 2022-03-18T12:09:48Z
date_published: 2019-01-02T00:00:00Z
date_updated: 2023-09-05T15:39:31Z
day: '02'
department:
- _id: TiBr
doi: 10.1007/s40993-018-0146-6
external_id:
arxiv:
- '1807.08986'
intvolume: ' 5'
keyword:
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1807.08986
month: '01'
oa: 1
oa_version: Preprint
publication: Research in Number Theory
publication_identifier:
eissn:
- 2363-9555
issn:
- 2522-0160
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Modular invariants for genus 3 hyperelliptic curves
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 5
year: '2019'
...
---
_id: '175'
abstract:
- lang: eng
text: An upper bound sieve for rational points on suitable varieties isdeveloped,
together with applications tocounting rational points in thin sets,to local solubility
in families, and to the notion of “friable” rational pointswith respect to divisors.
In the special case of quadrics, sharper estimates areobtained by developing a
version of the Selberg sieve for rational points.
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: Daniel
full_name: Loughran, Daniel
last_name: Loughran
citation:
ama: Browning TD, Loughran D. Sieving rational points on varieties. Transactions
of the American Mathematical Society. 2019;371(8):5757-5785. doi:10.1090/tran/7514
apa: Browning, T. D., & Loughran, D. (2019). Sieving rational points on varieties.
Transactions of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/tran/7514
chicago: Browning, Timothy D, and Daniel Loughran. “Sieving Rational Points on Varieties.”
Transactions of the American Mathematical Society. American Mathematical
Society, 2019. https://doi.org/10.1090/tran/7514.
ieee: T. D. Browning and D. Loughran, “Sieving rational points on varieties,” Transactions
of the American Mathematical Society, vol. 371, no. 8. American Mathematical
Society, pp. 5757–5785, 2019.
ista: Browning TD, Loughran D. 2019. Sieving rational points on varieties. Transactions
of the American Mathematical Society. 371(8), 5757–5785.
mla: Browning, Timothy D., and Daniel Loughran. “Sieving Rational Points on Varieties.”
Transactions of the American Mathematical Society, vol. 371, no. 8, American
Mathematical Society, 2019, pp. 5757–85, doi:10.1090/tran/7514.
short: T.D. Browning, D. Loughran, Transactions of the American Mathematical Society
371 (2019) 5757–5785.
date_created: 2018-12-11T11:45:01Z
date_published: 2019-04-15T00:00:00Z
date_updated: 2023-08-24T14:34:56Z
day: '15'
department:
- _id: TiBr
doi: 10.1090/tran/7514
external_id:
arxiv:
- '1705.01999'
isi:
- '000464034200019'
intvolume: ' 371'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.01999
month: '04'
oa: 1
oa_version: Preprint
page: 5757-5785
publication: Transactions of the American Mathematical Society
publication_identifier:
eissn:
- '10886850'
issn:
- '00029947'
publication_status: published
publisher: American Mathematical Society
publist_id: '7746'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sieving rational points on varieties
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 371
year: '2019'
...
---
_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'
...
---
_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'
...