---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21002'
abstract:
- lang: eng
text: The Davenport–Heilbronn method is a version of the circle method that was
developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn,
J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the
paper, together with an account of the development of the subject in the intervening
80 years.
acknowledgement: "The author is very grateful to Jörg Brüdern, Simon Rydin Myerson
and Trevor Wooley for their help and advice with preparing this survey, in addition
to Vinay Kumaraswamy, Victor Wang and the anonymous referee for useful comments
on an earlier draft. This work was supported by a FWF Grant (DOI 10.55776/P36278).\r\nOpen
Access funding provided by Institute of Science and Technology Austria/KEMÖ."
article_number: e70371
article_processing_charge: Yes (via OA deal)
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
citation:
ama: 'Browning TD. The Davenport–Heilbronn method: 80 years on. Journal of the
London Mathematical Society. 2026;113(1). doi:10.1112/jlms.70371'
apa: 'Browning, T. D. (2026). The Davenport–Heilbronn method: 80 years on. Journal
of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.70371'
chicago: 'Browning, Timothy D. “The Davenport–Heilbronn Method: 80 Years On.” Journal
of the London Mathematical Society. Wiley, 2026. https://doi.org/10.1112/jlms.70371.'
ieee: 'T. D. Browning, “The Davenport–Heilbronn method: 80 years on,” Journal
of the London Mathematical Society, vol. 113, no. 1. Wiley, 2026.'
ista: 'Browning TD. 2026. The Davenport–Heilbronn method: 80 years on. Journal of
the London Mathematical Society. 113(1), e70371.'
mla: 'Browning, Timothy D. “The Davenport–Heilbronn Method: 80 Years On.” Journal
of the London Mathematical Society, vol. 113, no. 1, e70371, Wiley, 2026,
doi:10.1112/jlms.70371.'
short: T.D. Browning, Journal of the London Mathematical Society 113 (2026).
corr_author: '1'
date_created: 2026-01-18T23:02:44Z
date_published: 2026-01-06T00:00:00Z
date_updated: 2026-01-19T08:23:15Z
day: '06'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1112/jlms.70371
file:
- access_level: open_access
checksum: 3b05bd625c81d038259a14f7e2ddd57c
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creator: dernst
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has_accepted_license: '1'
intvolume: ' 113'
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
issn:
- 0024-6107
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The Davenport–Heilbronn method: 80 years on'
tmp:
image: /images/cc_by.png
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user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20249'
abstract:
- lang: eng
text: We develop a heuristic for the density of integer points on affine cubic surfaces.
Our heuristic applies to smooth surfaces defined by cubic polynomials that are
log K3, but it can also be adjusted to handle singular cubic surfaces. We compare
our heuristic to Heath-Brown’s prediction for sums of three cubes, as well as
to asymptotic formulae in the literature around Zagier’s work on the Markoff cubic
surface, and work of Baragar and Umeda on further surfaces of Markoff-type. We
also test our heuristic against numerical data for several families of cubic surfaces.
acknowledgement: "The authors owe a debt of thanks to Yonatan Harpaz for asking about
circle method heuristics for log K3 surfaces. His contribution to the resulting
discussion is gratefully acknowledged. Thanks are also due to Andrew Sutherland
for help with numerical data for the equation x^3 + y^3 + z^3 = 1, together with
Alex Gamburd, Amit Ghosh, Peter Sarnak and Matteo Verzobio for their interest in
this paper. Special thanks are due to Victor Wang for helpful conversations about
the circle method heuristics and to the anonymous referee for several useful comments.
While working on this paper, the authors were supported by a FWF grant (DOI 10.55776/P32428),
and the first author was supported by a further FWF grant (DOI 10.55776/P36278)
and a grant from the School of Mathematics at the Institute for Advanced Study in
Princeton.\r\nOpen access funding provided by Institute of Science and Technology
(IST Austria)."
article_number: '81'
article_processing_charge: Yes (via OA deal)
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: Florian Alexander
full_name: Wilsch, Florian Alexander
id: 560601DA-8D36-11E9-A136-7AC1E5697425
last_name: Wilsch
orcid: 0000-0001-7302-8256
citation:
ama: 'Browning TD, Wilsch FA. Integral points on cubic surfaces: heuristics and
numerics. Selecta Mathematica New Series. 2025;31(4). doi:10.1007/s00029-025-01074-1'
apa: 'Browning, T. D., & Wilsch, F. A. (2025). Integral points on cubic surfaces:
heuristics and numerics. Selecta Mathematica New Series. Springer Nature.
https://doi.org/10.1007/s00029-025-01074-1'
chicago: 'Browning, Timothy D, and Florian Alexander Wilsch. “Integral Points on
Cubic Surfaces: Heuristics and Numerics.” Selecta Mathematica New Series.
Springer Nature, 2025. https://doi.org/10.1007/s00029-025-01074-1.'
ieee: 'T. D. Browning and F. A. Wilsch, “Integral points on cubic surfaces: heuristics
and numerics,” Selecta Mathematica New Series, vol. 31, no. 4. Springer
Nature, 2025.'
ista: 'Browning TD, Wilsch FA. 2025. Integral points on cubic surfaces: heuristics
and numerics. Selecta Mathematica New Series. 31(4), 81.'
mla: 'Browning, Timothy D., and Florian Alexander Wilsch. “Integral Points on Cubic
Surfaces: Heuristics and Numerics.” Selecta Mathematica New Series, vol.
31, no. 4, 81, Springer Nature, 2025, doi:10.1007/s00029-025-01074-1.'
short: T.D. Browning, F.A. Wilsch, Selecta Mathematica New Series 31 (2025).
corr_author: '1'
date_created: 2025-08-31T22:01:31Z
date_published: 2025-09-01T00:00:00Z
date_updated: 2025-09-30T14:29:25Z
day: '01'
ddc:
- '500'
department:
- _id: TiBr
doi: 10.1007/s00029-025-01074-1
external_id:
arxiv:
- '2407.16315'
isi:
- '001552779800001'
file:
- access_level: open_access
checksum: 89352f1f7e8d2b367ae5f4e9bf9eb1f5
content_type: application/pdf
creator: dernst
date_created: 2025-09-03T06:44:44Z
date_updated: 2025-09-03T06:44:44Z
file_id: '20281'
file_name: 2025_SelectaMathematica_Browning.pdf
file_size: 2484757
relation: main_file
success: 1
file_date_updated: 2025-09-03T06:44:44Z
has_accepted_license: '1'
intvolume: ' 31'
isi: 1
issue: '4'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
publication: Selecta Mathematica New Series
publication_identifier:
eissn:
- 1420-9020
issn:
- 1022-1824
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Integral points on cubic surfaces: heuristics and numerics'
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: 31
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20367'
abstract:
- lang: eng
text: We prove upper and lower bounds on the number of pairs of commuting n x n
matrices with integer entries in [-T, T], as T -> . Our work uses Fourier analysis
and leads to an analysis of exponential sums involving matrices over finite fields.
These are bounded by combining a stratification result of Fouvry and Katz with
a new result about the flatness of the commutator Lie bracket.
acknowledgement: The authors are very grateful to Alina Ostafe, Matthew Satriano and
Igor Shparlinski for drawing their attention to this problem and for useful comments,
and to Michael Larsen and Peter Sarnak for their helpful correspondence. We also
thank the referee for their valuable input. While working on this paper the first
author was supported by a FWF grant (DOI 10.55776/P36278), the second author by
a Sloan Research Fellowship, and the third author by the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 101034413. Open access funding provided by Institute of Science and Technology
(IST Austria).
article_processing_charge: Yes (via OA deal)
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
- first_name: Victor
full_name: Wang, Victor
id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
last_name: Wang
orcid: 0000-0002-0704-7026
citation:
ama: Browning TD, Sawin W, Wang V. Pairs of commuting integer matrices. Mathematische
Annalen. 2025;393:1863–1880. doi:10.1007/s00208-025-03285-5
apa: Browning, T. D., Sawin, W., & Wang, V. (2025). Pairs of commuting integer
matrices. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-025-03285-5
chicago: Browning, Timothy D, Will Sawin, and Victor Wang. “Pairs of Commuting Integer
Matrices.” Mathematische Annalen. Springer Nature, 2025. https://doi.org/10.1007/s00208-025-03285-5.
ieee: T. D. Browning, W. Sawin, and V. Wang, “Pairs of commuting integer matrices,”
Mathematische Annalen, vol. 393. Springer Nature, pp. 1863–1880, 2025.
ista: Browning TD, Sawin W, Wang V. 2025. Pairs of commuting integer matrices. Mathematische
Annalen. 393, 1863–1880.
mla: Browning, Timothy D., et al. “Pairs of Commuting Integer Matrices.” Mathematische
Annalen, vol. 393, Springer Nature, 2025, pp. 1863–1880, doi:10.1007/s00208-025-03285-5.
short: T.D. Browning, W. Sawin, V. Wang, Mathematische Annalen 393 (2025) 1863–1880.
corr_author: '1'
date_created: 2025-09-21T22:01:31Z
date_published: 2025-10-01T00:00:00Z
date_updated: 2026-01-05T13:15:53Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00208-025-03285-5
ec_funded: 1
external_id:
arxiv:
- '2409.01920'
isi:
- '001567740200001'
file:
- access_level: open_access
checksum: 1e94da1a67306e03c8e0086518faf4bc
content_type: application/pdf
creator: dernst
date_created: 2026-01-05T13:15:44Z
date_updated: 2026-01-05T13:15:44Z
file_id: '20950'
file_name: 2025_MathAnnalen_Browning.pdf
file_size: 337505
relation: main_file
success: 1
file_date_updated: 2026-01-05T13:15:44Z
has_accepted_license: '1'
intvolume: ' 393'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1863–1880
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pairs of commuting integer matrices
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 393
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19776'
abstract:
- lang: eng
text: We use the circle method to prove that a density 1 of elements in Fq[t] are
representable as a sum of three cubes of essentially minimal degree from Fq[t],
assuming the Ratios Conjecture and that char(Fq)>3. Roughly speaking, to do so,
we upgrade an order of magnitude result to a full asymptotic formula that was
conjectured by Hooley in the number field setting.
acknowledgement: We thank Alexandra Florea for discussions on cubic Gauss sums over
function fields, in addition to the anonymous referee for helpful comments. While
working on this paper the first two authors were supported by a FWF grant (DOI 10.55776/P36278)
and the third author was supported by the European Union’s Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.
Open access funding provided by Institute of Science and Technology (IST Austria).
article_number: '65'
article_processing_charge: Yes (via OA deal)
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: Jakob
full_name: Glas, Jakob
id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb
last_name: Glas
- first_name: Victor
full_name: Wang, Victor
id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
last_name: Wang
orcid: 0000-0002-0704-7026
citation:
ama: Browning TD, Glas J, Wang V. Optimal sums of three cubes in Fq[t]. Mathematische
Zeitschrift. 2025;310(4). doi:10.1007/s00209-025-03765-z
apa: Browning, T. D., Glas, J., & Wang, V. (2025). Optimal sums of three cubes
in Fq[t]. Mathematische Zeitschrift. Springer Nature. https://doi.org/10.1007/s00209-025-03765-z
chicago: Browning, Timothy D, Jakob Glas, and Victor Wang. “Optimal Sums of Three
Cubes in Fq[T].” Mathematische Zeitschrift. Springer Nature, 2025. https://doi.org/10.1007/s00209-025-03765-z.
ieee: T. D. Browning, J. Glas, and V. Wang, “Optimal sums of three cubes in Fq[t],”
Mathematische Zeitschrift, vol. 310, no. 4. Springer Nature, 2025.
ista: Browning TD, Glas J, Wang V. 2025. Optimal sums of three cubes in Fq[t]. Mathematische
Zeitschrift. 310(4), 65.
mla: Browning, Timothy D., et al. “Optimal Sums of Three Cubes in Fq[T].” Mathematische
Zeitschrift, vol. 310, no. 4, 65, Springer Nature, 2025, doi:10.1007/s00209-025-03765-z.
short: T.D. Browning, J. Glas, V. Wang, Mathematische Zeitschrift 310 (2025).
corr_author: '1'
date_created: 2025-06-03T07:30:21Z
date_published: 2025-05-23T00:00:00Z
date_updated: 2025-09-30T12:43:41Z
day: '23'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00209-025-03765-z
ec_funded: 1
external_id:
arxiv:
- '2408.03668 '
isi:
- '001494367000001'
file:
- access_level: open_access
checksum: 6f71e25740c28257bf89b8bf116c2b4d
content_type: application/pdf
creator: dernst
date_created: 2025-06-03T08:28:14Z
date_updated: 2025-06-03T08:28:14Z
file_id: '19782'
file_name: 2025_MathZeitschrift_Browning.pdf
file_size: 461622
relation: main_file
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file_date_updated: 2025-06-03T08:28:14Z
has_accepted_license: '1'
intvolume: ' 310'
isi: 1
issue: '4'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
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: Optimal sums of three cubes in Fq[t]
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: 310
year: '2025'
...
---
OA_place: publisher
OA_type: diamond
_id: '21003'
abstract:
- lang: eng
text: We extend work of Heath-Brown and Salberger, based on the determinant method,
to provide a uniform upper bound for the number of integral points of bounded
height on an affine surface, which are subject to a polynomial congruence condition.
This is applied to get a new uniform bound for points on diagonal quadric surfaces,
and to a problem about the representation of integers as a sum of four unlike
powers.
acknowledgement: "Supported by FWF grant (DOI 10.55776/P36278), Supported by European
Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie
Grant\r\nAgreement No. 101034413."
article_number: '12'
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: Matteo
full_name: Verzobio, Matteo
id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
last_name: Verzobio
orcid: 0000-0002-0854-0306
citation:
ama: Browning TD, Verzobio M. Counting integer points on affine surfaces with a
side condition. Discrete Analysis. 2025;2025. doi:10.19086/da.143787
apa: 'Browning, T. D., & Verzobio, M. (2025). Counting integer points on affine
surfaces with a side condition. Discrete Analysis. Cambridge: Alliance
of Diamond Open Access Journals. https://doi.org/10.19086/da.143787'
chicago: 'Browning, Timothy D, and Matteo Verzobio. “Counting Integer Points on
Affine Surfaces with a Side Condition.” Discrete Analysis. Cambridge: Alliance
of Diamond Open Access Journals, 2025. https://doi.org/10.19086/da.143787.'
ieee: 'T. D. Browning and M. Verzobio, “Counting integer points on affine surfaces
with a side condition,” Discrete Analysis, vol. 2025. Cambridge: Alliance
of Diamond Open Access Journals, 2025.'
ista: Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces
with a side condition. Discrete Analysis. 2025, 12.
mla: 'Browning, Timothy D., and Matteo Verzobio. “Counting Integer Points on Affine
Surfaces with a Side Condition.” Discrete Analysis, vol. 2025, 12, Cambridge:
Alliance of Diamond Open Access Journals, 2025, doi:10.19086/da.143787.'
short: T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025).
corr_author: '1'
date_created: 2026-01-18T23:02:44Z
date_published: 2025-09-01T00:00:00Z
date_updated: 2026-02-12T08:03:12Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.19086/da.143787
ec_funded: 1
external_id:
arxiv:
- '2408.11453'
file:
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checksum: 3d38e850b40f3e1abbfd30073bd4388a
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creator: dernst
date_created: 2026-02-12T07:50:47Z
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file_name: 2025_DiscreteAnalysis_Browning.pdf
file_size: 393625
relation: main_file
success: 1
file_date_updated: 2026-02-12T07:50:47Z
has_accepted_license: '1'
intvolume: ' 2025'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Discrete Analysis
publication_identifier:
eissn:
- 2397-3129
publication_status: published
publisher: 'Cambridge: Alliance of Diamond Open Access Journals'
scopus_import: '1'
status: public
title: Counting integer points on affine surfaces with a side condition
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short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2025
year: '2025'
...
---
OA_place: publisher
OA_type: diamond
PlanS_conform: '1'
_id: '21244'
abstract:
- lang: eng
text: 'Given a family of varieties over the projective line, we study the density
of fibres that are everywhere locally soluble in the case that components of higher
multiplicity are allowed. We use log geometry to formulate a new sparsity criterion
for the existence of everywhere locally soluble fibres and formulate new conjectures
that generalise previous work of Loughran and Smeets. These conjectures involve
geometric invariants of the associated multiplicity orbifolds on the base of the
fibration in the spirit of Campana. We give evidence for the conjectures by providing
an assortment of bounds using Chebotarev’s theorem and sieve methods, with most
of the evidence involving upper bounds. '
acknowledgement: We are very grateful to Tim Santens for useful conversations and
to the anonymous referees for numerous pertinent remarks. While working on this
paper, Browning was supported by a FWF grant (DOI 10.55776/P32428), Lyczak was supported
by UKRI MR/V021362/1, and Smeets was supported by grant G0B1721N of the Fund for
Scientific Research – Flanders.
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: Julian
full_name: Lyczak, Julian
last_name: Lyczak
- first_name: Arne
full_name: Smeets, Arne
last_name: Smeets
citation:
ama: Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with
multiple fibres. Algebra & Number Theory. 2025;19(10):2049-2090. doi:10.2140/ant.2025.19.2049
apa: Browning, T. D., Lyczak, J., & Smeets, A. (2025). Paucity of rational points
on fibrations with multiple fibres. Algebra & Number Theory. Mathematical
Sciences Publishers. https://doi.org/10.2140/ant.2025.19.2049
chicago: Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational
Points on Fibrations with Multiple Fibres.” Algebra & Number Theory.
Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/ant.2025.19.2049.
ieee: T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations
with multiple fibres,” Algebra & Number Theory, vol. 19, no. 10. Mathematical
Sciences Publishers, pp. 2049–2090, 2025.
ista: Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations
with multiple fibres. Algebra & Number Theory. 19(10), 2049–2090.
mla: Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with
Multiple Fibres.” Algebra & Number Theory, vol. 19, no. 10, Mathematical
Sciences Publishers, 2025, pp. 2049–90, doi:10.2140/ant.2025.19.2049.
short: T.D. Browning, J. Lyczak, A. Smeets, Algebra & Number Theory 19 (2025)
2049–2090.
corr_author: '1'
date_created: 2026-02-16T15:22:19Z
date_published: 2025-09-05T00:00:00Z
date_updated: 2026-02-17T11:59:57Z
day: '05'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.2140/ant.2025.19.2049
external_id:
arxiv:
- '2310.01135'
file:
- access_level: open_access
checksum: e50a60a4303b81563f7adbcadbe2e986
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creator: dernst
date_created: 2026-02-17T11:56:20Z
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has_accepted_license: '1'
intvolume: ' 19'
issue: '10'
language:
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month: '09'
oa: 1
oa_version: Published Version
page: 2049-2090
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Algebra & Number Theory
publication_identifier:
eissn:
- 1944-7833
issn:
- 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
status: public
title: Paucity of rational points on fibrations with multiple fibres
tmp:
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...
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OA_place: publisher
OA_type: gold
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abstract:
- lang: eng
text: "The large sieve is used to estimate the density of quadratic polynomials
Q ∈ Z[x],\r\nsuch that there exists an odd degree polynomial defined over Z which
has resultant ±1 with Q.\r\nGiven a monic polynomial R ∈ Z[x] of odd degree, this
is used to show that for almost all\r\nquadratic polynomials Q ∈ Z[x], there exists
a prime p such that Q and R share a common\r\nroot in Fp. Using recent work of
Landesman, an application to the average size of the odd part\r\nof the class
group of quadratic number fields is also given"
- lang: fre
text: ' Le grand crible est utilisé pour estimer la densité des polynômes quadratiques
Q ∈ Z[x] tels qu’il existe un polynôme de degré impair défini sur Z dont le résultant
avec Q est égal à ±1. Étant donné un polynôme unitaire R ∈ Z[x] de degré impair,
on s’en sert pour montrer que, pour presque tous les polynômes quadratiques Q
∈ Z[x], il existe un nombre premier p tel que Q et R aient une racine commune
dans Fp. En utilisant des travaux récents de Landesman, on obtient également une
application concernant la taille moyenne de la partie impaire du groupe de classe
des corps quadratiques.'
acknowledgement: While working on this paper, the first author was supported by a
FWF grant (DOI 10.55776/P36278).
article_processing_charge: Yes
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: Yik Tung
full_name: Chan, Yik Tung
id: c4c0afc8-9262-11ed-9231-d8b0bc743af1
last_name: Chan
orcid: 0000-0001-8467-4106
citation:
ama: Browning TD, Chan S. Solubility of a resultant equation and applications. Journal
de l’ecole polytechnique mathematiques. 2025;12:1677-1691. doi:10.5802/jep.320
apa: Browning, T. D., & Chan, S. (2025). Solubility of a resultant equation
and applications. Journal de l’ecole Polytechnique Mathematiques. Ecole
polytechnique. https://doi.org/10.5802/jep.320
chicago: Browning, Timothy D, and Stephanie Chan. “Solubility of a Resultant Equation
and Applications.” Journal de l’ecole Polytechnique Mathematiques. Ecole
polytechnique, 2025. https://doi.org/10.5802/jep.320.
ieee: T. D. Browning and S. Chan, “Solubility of a resultant equation and applications,”
Journal de l’ecole polytechnique mathematiques, vol. 12. Ecole polytechnique,
pp. 1677–1691, 2025.
ista: Browning TD, Chan S. 2025. Solubility of a resultant equation and applications.
Journal de l’ecole polytechnique mathematiques. 12, 1677–1691.
mla: Browning, Timothy D., and Stephanie Chan. “Solubility of a Resultant Equation
and Applications.” Journal de l’ecole Polytechnique Mathematiques, vol.
12, Ecole polytechnique, 2025, pp. 1677–91, doi:10.5802/jep.320.
short: T.D. Browning, S. Chan, Journal de l’ecole Polytechnique Mathematiques 12
(2025) 1677–1691.
corr_author: '1'
date_created: 2026-02-22T23:01:36Z
date_published: 2025-10-21T00:00:00Z
date_updated: 2026-02-24T07:57:53Z
day: '21'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.5802/jep.320
external_id:
arxiv:
- '2411.09264'
file:
- access_level: open_access
checksum: 828577ea48ac6109d3e9dd1aeddd45c4
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creator: dernst
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file_name: 2025_JEP_Browning.pdf
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file_date_updated: 2026-02-24T07:56:34Z
has_accepted_license: '1'
intvolume: ' 12'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1677-1691
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
publication: Journal de l'ecole polytechnique mathematiques
publication_identifier:
eissn:
- 2270-518X
issn:
- 2429-7100
publication_status: published
publisher: Ecole polytechnique
quality_controlled: '1'
scopus_import: '1'
status: public
title: Solubility of a resultant equation and applications
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)
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12
year: '2025'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: diamond
_id: '21266'
abstract:
- lang: eng
text: "For a given elliptic curve E in short Weierstrass form, we show that almost
all quadratic twists E \r\nD have no integral points, as D ranges over square-free
integers ordered by size. Our result is conditional on a weak form of the Hall–Lang
conjecture in the case that E has partial 2-torsion. The proof uses a correspondence
of Mordell and the reduction theory of binary quartic forms in order to transfer
the problem to counting rational points of bounded height on a certain singular
cubic surface, together with extensive use of cancellation in character sum estimates,
drawn from Heath-Brown’s analysis of Selmer group statistics for the congruent
number curve."
acknowledgement: The authors are grateful to Roger Heath-Brown and to the anonymous
referees for useful comments. The first author was supported by an FWF grant (DOI
10.55776/P36278).
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: Yik Tung
full_name: Chan, Yik Tung
id: c4c0afc8-9262-11ed-9231-d8b0bc743af1
last_name: Chan
orcid: 0000-0001-8467-4106
citation:
ama: Browning TD, Chan S. Almost all quadratic twists of an elliptic curve have
no integral points. Journal of the European Mathematical Society. 2025.
doi:10.4171/jems/1704
apa: Browning, T. D., & Chan, S. (2025). Almost all quadratic twists of an elliptic
curve have no integral points. Journal of the European Mathematical Society.
European Mathematical Society Press. https://doi.org/10.4171/jems/1704
chicago: Browning, Timothy D, and Stephanie Chan. “Almost All Quadratic Twists of
an Elliptic Curve Have No Integral Points.” Journal of the European Mathematical
Society. European Mathematical Society Press, 2025. https://doi.org/10.4171/jems/1704.
ieee: T. D. Browning and S. Chan, “Almost all quadratic twists of an elliptic curve
have no integral points,” Journal of the European Mathematical Society.
European Mathematical Society Press, 2025.
ista: Browning TD, Chan S. 2025. Almost all quadratic twists of an elliptic curve
have no integral points. Journal of the European Mathematical Society.
mla: Browning, Timothy D., and Stephanie Chan. “Almost All Quadratic Twists of an
Elliptic Curve Have No Integral Points.” Journal of the European Mathematical
Society, European Mathematical Society Press, 2025, doi:10.4171/jems/1704.
short: T.D. Browning, S. Chan, Journal of the European Mathematical Society (2025).
corr_author: '1'
date_created: 2026-02-17T07:46:26Z
date_published: 2025-09-17T00:00:00Z
date_updated: 2026-06-18T18:31:51Z
day: '17'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.4171/jems/1704
external_id:
arxiv:
- '2401.04375'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.4171/JEMS/1704
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
publication: Journal of the European Mathematical Society
publication_identifier:
eissn:
- 1435-9863
issn:
- 1435-9855
publication_status: epub_ahead
publisher: European Mathematical Society Press
quality_controlled: '1'
status: public
title: Almost all quadratic twists of an elliptic curve have no integral points
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19051'
abstract:
- lang: eng
text: This paper corrects an error in an earlier work of the author.
article_processing_charge: Yes (via OA deal)
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
citation:
ama: Browning TD. The polynomial sieve and equal sums of like polynomials. International
Mathematics Research Notices. 2024;2024(13):10165-10168. doi:10.1093/imrn/rnae066
apa: Browning, T. D. (2024). The polynomial sieve and equal sums of like polynomials.
International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae066
chicago: Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.”
International Mathematics Research Notices. Oxford University Press, 2024.
https://doi.org/10.1093/imrn/rnae066.
ieee: T. D. Browning, “The polynomial sieve and equal sums of like polynomials,”
International Mathematics Research Notices, vol. 2024, no. 13. Oxford University
Press, pp. 10165–10168, 2024.
ista: Browning TD. 2024. The polynomial sieve and equal sums of like polynomials.
International Mathematics Research Notices. 2024(13), 10165–10168.
mla: Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.”
International Mathematics Research Notices, vol. 2024, no. 13, Oxford University
Press, 2024, pp. 10165–68, doi:10.1093/imrn/rnae066.
short: T.D. Browning, International Mathematics Research Notices 2024 (2024) 10165–10168.
corr_author: '1'
date_created: 2025-02-18T07:15:50Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-09T12:16:45Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1093/imrn/rnae066
external_id:
isi:
- '001196957300001'
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checksum: b625b8adf018d2a97591813c1fc17b96
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creator: dernst
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date_updated: 2025-02-18T07:56:36Z
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file_size: 205750
relation: main_file
success: 1
file_date_updated: 2025-02-18T07:56:36Z
has_accepted_license: '1'
intvolume: ' 2024'
isi: 1
issue: '13'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 10165-10168
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
related_material:
record:
- id: '254'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The polynomial sieve and equal sums of like polynomials
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image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 2024
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15312'
abstract:
- lang: eng
text: The question of whether or not a given integral polynomial takes infinitely
many square-free values has only been addressed unconditionally for polynomials
of degree at most 3. We address this question, on average, for polynomials of
arbitrary 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: Igor E.
full_name: Shparlinski, Igor E.
last_name: Shparlinski
citation:
ama: Browning TD, Shparlinski IE. Square-free values of random polynomials. Journal
of Number Theory. 2024;261:220-240. doi:10.1016/j.jnt.2024.02.013
apa: Browning, T. D., & Shparlinski, I. E. (2024). Square-free values of random
polynomials. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2024.02.013
chicago: Browning, Timothy D, and Igor E. Shparlinski. “Square-Free Values of Random
Polynomials.” Journal of Number Theory. Elsevier, 2024. https://doi.org/10.1016/j.jnt.2024.02.013.
ieee: T. D. Browning and I. E. Shparlinski, “Square-free values of random polynomials,”
Journal of Number Theory, vol. 261. Elsevier, pp. 220–240, 2024.
ista: Browning TD, Shparlinski IE. 2024. Square-free values of random polynomials.
Journal of Number Theory. 261, 220–240.
mla: Browning, Timothy D., and Igor E. Shparlinski. “Square-Free Values of Random
Polynomials.” Journal of Number Theory, vol. 261, Elsevier, 2024, pp. 220–40,
doi:10.1016/j.jnt.2024.02.013.
short: T.D. Browning, I.E. Shparlinski, Journal of Number Theory 261 (2024) 220–240.
corr_author: '1'
date_created: 2024-04-14T22:01:00Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-04T13:47:43Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1016/j.jnt.2024.02.013
external_id:
arxiv:
- '2305.15493'
isi:
- '001220725000001'
file:
- access_level: open_access
checksum: 614032802febde0aa8e904e9a8ef99ab
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T09:00:02Z
date_updated: 2025-01-09T09:00:02Z
file_id: '18794'
file_name: 2024_JourNumberTheory_Browning.pdf
file_size: 394850
relation: main_file
success: 1
file_date_updated: 2025-01-09T09:00:02Z
has_accepted_license: '1'
intvolume: ' 261'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 220-240
publication: Journal of Number Theory
publication_identifier:
issn:
- 0022-314X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Square-free values of random polynomials
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: 261
year: '2024'
...
---
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'
date_created: 2024-04-21T22:00:53Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-04T13:41:19Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00208-024-02854-4
external_id:
arxiv:
- '2204.09322'
isi:
- '001204670500001'
file:
- access_level: open_access
checksum: 5dd51531deb1e4760c38c3c0c7d5aedc
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T09:08:14Z
date_updated: 2025-01-09T09:08:14Z
file_id: '18796'
file_name: 2024_MathAnnalen_Bonolis.pdf
file_size: 1019116
relation: main_file
success: 1
file_date_updated: 2025-01-09T09:08:14Z
has_accepted_license: '1'
intvolume: ' 390'
isi: 1
language:
- iso: eng
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'
scopus_import: '1'
status: public
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'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15338'
abstract:
- lang: eng
text: We introduce a new class of generalised quadratic forms over totally real
number fields, which is rich enough to capture the arithmetic of arbitrary systems
of quadrics over the rational numbers. We explore this connection through a version
of the Hardy–Littlewood circle method over number fields.
acknowledgement: The authors are grateful to Jayce Getz for asking questions that
set this project in motion and to the anonymous referee for useful comments. T.B.
was supported by a FWF grant (DOI 10.55776/P32428) and by a grant from the Institute
for Advanced Study School of Mathematics. L.B.P. was partially supported by NSF
DMS-2200470 and DMS-1652173, and thanks the Hausdorff Centre for Mathematics for
hosting research visits.
article_processing_charge: Yes (via OA deal)
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: Lillian B.
full_name: Pierce, Lillian B.
last_name: Pierce
- first_name: Damaris
full_name: Schindler, Damaris
last_name: Schindler
citation:
ama: Browning TD, Pierce LB, Schindler D. Generalised quadratic forms over totally
real number fields. Journal of the Institute of Mathematics of Jussieu.
2024;23(6):2859-2912. doi:10.1017/S1474748024000161
apa: Browning, T. D., Pierce, L. B., & Schindler, D. (2024). Generalised quadratic
forms over totally real number fields. Journal of the Institute of Mathematics
of Jussieu. Cambridge University Press. https://doi.org/10.1017/S1474748024000161
chicago: Browning, Timothy D, Lillian B. Pierce, and Damaris Schindler. “Generalised
Quadratic Forms over Totally Real Number Fields.” Journal of the Institute
of Mathematics of Jussieu. Cambridge University Press, 2024. https://doi.org/10.1017/S1474748024000161.
ieee: T. D. Browning, L. B. Pierce, and D. Schindler, “Generalised quadratic forms
over totally real number fields,” Journal of the Institute of Mathematics of
Jussieu, vol. 23, no. 6. Cambridge University Press, pp. 2859–2912, 2024.
ista: Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over
totally real number fields. Journal of the Institute of Mathematics of Jussieu.
23(6), 2859–2912.
mla: Browning, Timothy D., et al. “Generalised Quadratic Forms over Totally Real
Number Fields.” Journal of the Institute of Mathematics of Jussieu, vol.
23, no. 6, Cambridge University Press, 2024, pp. 2859–912, doi:10.1017/S1474748024000161.
short: T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics
of Jussieu 23 (2024) 2859–2912.
corr_author: '1'
date_created: 2024-04-21T22:00:53Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-04T13:44:16Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/S1474748024000161
external_id:
arxiv:
- '2212.11038'
isi:
- '001200337400001'
file:
- access_level: open_access
checksum: b300541d581a71d92314df5ae8c4cc09
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:56:33Z
date_updated: 2025-01-09T08:56:33Z
file_id: '18793'
file_name: 2024_JournInstMathJussieu_Browning.pdf
file_size: 690974
relation: main_file
success: 1
file_date_updated: 2025-01-09T08:56:33Z
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '6'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 2859-2912
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Journal of the Institute of Mathematics of Jussieu
publication_identifier:
eissn:
- 1475-3030
issn:
- 1474-7480
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Generalised quadratic forms over totally real number fields
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: 23
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '17323'
abstract:
- lang: eng
text: We investigate strong divisibility sequences and produce lower and upper bounds
for the density of integers in the sequence that only have (somewhat) large prime
factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility
sequences, discussing the limitations of our methods. At the end of the paper,
there is an appendix by Sandro Bettin on divisor closed sets that we use to study
the density of prime terms that appear in strong divisibility sequences.
acknowledgement: The authors are very grateful to Andrew Granville, Dimitris Koukoulopoulos,
Davide Lombardo,Florian Luca, Igor Shparlinski and Joni Teräväinen for useful comments.
While working on thispaper, the first author was supported by a FWF Grant (DOI 10.55776/P36278)
and the secondauthor was supported by the European Union’s Horizon 2020 research
and innovation programunder the Marie Skłodowska-Curie Grant Agreement Number 101034413.
article_number: e12269
article_processing_charge: Yes (via OA deal)
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: Matteo
full_name: Verzobio, Matteo
id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
last_name: Verzobio
orcid: 0000-0002-0854-0306
citation:
ama: Browning TD, Verzobio M. Strong divisibility sequences and sieve methods. Mathematika.
2024;70(4). doi:10.1112/mtk.12269
apa: Browning, T. D., & Verzobio, M. (2024). Strong divisibility sequences and
sieve methods. Mathematika. London Mathematical Society. https://doi.org/10.1112/mtk.12269
chicago: Browning, Timothy D, and Matteo Verzobio. “Strong Divisibility Sequences
and Sieve Methods.” Mathematika. London Mathematical Society, 2024. https://doi.org/10.1112/mtk.12269.
ieee: T. D. Browning and M. Verzobio, “Strong divisibility sequences and sieve methods,”
Mathematika, vol. 70, no. 4. London Mathematical Society, 2024.
ista: Browning TD, Verzobio M. 2024. Strong divisibility sequences and sieve methods.
Mathematika. 70(4), e12269.
mla: Browning, Timothy D., and Matteo Verzobio. “Strong Divisibility Sequences and
Sieve Methods.” Mathematika, vol. 70, no. 4, e12269, London Mathematical
Society, 2024, doi:10.1112/mtk.12269.
short: T.D. Browning, M. Verzobio, Mathematika 70 (2024).
corr_author: '1'
date_created: 2024-07-28T22:01:08Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2025-09-08T08:44:11Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1112/mtk.12269
ec_funded: 1
external_id:
isi:
- '001273912800001'
file:
- access_level: open_access
checksum: 0b1518bdc1a901413005c19202cfa497
content_type: application/pdf
creator: dernst
date_created: 2025-01-13T11:06:25Z
date_updated: 2025-01-13T11:06:25Z
file_id: '18842'
file_name: 2024_Mathematika_Browning.pdf
file_size: 273006
relation: main_file
success: 1
file_date_updated: 2025-01-13T11:06:25Z
has_accepted_license: '1'
intvolume: ' 70'
isi: 1
issue: '4'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Mathematika
publication_identifier:
eissn:
- 2041-7942
issn:
- 0025-5793
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Strong divisibility sequences and sieve methods
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: 70
year: '2024'
...
---
_id: '12916'
abstract:
- lang: eng
text: "We apply a variant of the square-sieve to produce an upper bound for the
number of rational points of bounded height on a family of surfaces that admit
a fibration over P1 whose general fibre is a hyperelliptic curve. The implied
constant does not depend on the coefficients of the polynomial defining the surface.\r\n"
article_processing_charge: No
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
citation:
ama: Bonolis D, Browning TD. Uniform bounds for rational points on hyperelliptic
fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze.
2023;24(1):173-204. doi:10.2422/2036-2145.202010_018
apa: Bonolis, D., & Browning, T. D. (2023). Uniform bounds for rational points
on hyperelliptic fibrations. Annali Della Scuola Normale Superiore Di Pisa
- Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale. https://doi.org/10.2422/2036-2145.202010_018
chicago: Bonolis, Dante, and Timothy D Browning. “Uniform Bounds for Rational Points
on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa
- Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale, 2023.
https://doi.org/10.2422/2036-2145.202010_018.
ieee: D. Bonolis and T. D. Browning, “Uniform bounds for rational points on hyperelliptic
fibrations,” Annali della Scuola Normale Superiore di Pisa - Classe di Scienze,
vol. 24, no. 1. Scuola Normale Superiore - Edizioni della Normale, pp. 173–204,
2023.
ista: Bonolis D, Browning TD. 2023. Uniform bounds for rational points on hyperelliptic
fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze.
24(1), 173–204.
mla: Bonolis, Dante, and Timothy D. Browning. “Uniform Bounds for Rational Points
on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa
- Classe Di Scienze, vol. 24, no. 1, Scuola Normale Superiore - Edizioni della
Normale, 2023, pp. 173–204, doi:10.2422/2036-2145.202010_018.
short: D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa
- Classe Di Scienze 24 (2023) 173–204.
corr_author: '1'
date_created: 2023-05-07T22:01:04Z
date_published: 2023-02-16T00:00:00Z
date_updated: 2024-10-09T21:05:05Z
day: '16'
department:
- _id: TiBr
doi: 10.2422/2036-2145.202010_018
external_id:
arxiv:
- '2007.14182'
intvolume: ' 24'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2007.14182
month: '02'
oa: 1
oa_version: Preprint
page: 173-204
publication: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
publication_identifier:
eissn:
- 2036-2145
issn:
- 0391-173X
publication_status: published
publisher: Scuola Normale Superiore - Edizioni della Normale
quality_controlled: '1'
scopus_import: '1'
status: public
title: Uniform bounds for rational points on hyperelliptic fibrations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '13091'
abstract:
- lang: eng
text: We use a function field version of the Hardy–Littlewood circle method to study
the locus of free rational curves on an arbitrary smooth projective hypersurface
of sufficiently low degree. On the one hand this allows us to bound the dimension
of the singular locus of the moduli space of rational curves on such hypersurfaces
and, on the other hand, it sheds light on Peyre’s reformulation of the Batyrev–Manin
conjecture in terms of slopes with respect to the tangent bundle.
acknowledgement: The authors are grateful to Paul Nelson, Per Salberger and Jason
Starr for useful comments. While working on this paper the first author was supported
by EPRSC grant EP/P026710/1. The research was partially conducted during the period
the second author served as a Clay Research Fellow, and partially conducted during
the period he was supported by Dr. Max Rössler, the Walter Haefner Foundation and
the ETH Zurich Foundation.
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 curves on low degree hypersurfaces and
the circle method. Algebra and Number Theory. 2023;17(3):719-748. doi:10.2140/ant.2023.17.719
apa: Browning, T. D., & Sawin, W. (2023). Free rational curves on low degree
hypersurfaces and the circle method. Algebra and Number Theory. Mathematical
Sciences Publishers. https://doi.org/10.2140/ant.2023.17.719
chicago: Browning, Timothy D, and Will Sawin. “Free Rational Curves on Low Degree
Hypersurfaces and the Circle Method.” Algebra and Number Theory. Mathematical
Sciences Publishers, 2023. https://doi.org/10.2140/ant.2023.17.719.
ieee: T. D. Browning and W. Sawin, “Free rational curves on low degree hypersurfaces
and the circle method,” Algebra and Number Theory, vol. 17, no. 3. Mathematical
Sciences Publishers, pp. 719–748, 2023.
ista: Browning TD, Sawin W. 2023. Free rational curves on low degree hypersurfaces
and the circle method. Algebra and Number Theory. 17(3), 719–748.
mla: Browning, Timothy D., and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces
and the Circle Method.” Algebra and Number Theory, vol. 17, no. 3, Mathematical
Sciences Publishers, 2023, pp. 719–48, doi:10.2140/ant.2023.17.719.
short: T.D. Browning, W. Sawin, Algebra and Number Theory 17 (2023) 719–748.
corr_author: '1'
date_created: 2023-05-28T22:01:02Z
date_published: 2023-04-12T00:00:00Z
date_updated: 2025-04-14T09:25:44Z
day: '12'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.2140/ant.2023.17.719
external_id:
arxiv:
- '1810.06882'
isi:
- '000996014700004'
file:
- access_level: open_access
checksum: 5d5d67b235905650e33cf7065d7583b4
content_type: application/pdf
creator: dernst
date_created: 2023-05-30T08:05:22Z
date_updated: 2023-05-30T08:05:22Z
file_id: '13101'
file_name: 2023_AlgebraNumberTheory_Browning.pdf
file_size: 1430719
relation: main_file
success: 1
file_date_updated: 2023-05-30T08:05:22Z
has_accepted_license: '1'
intvolume: ' 17'
isi: 1
issue: '3'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 719-748
project:
- _id: 26A8D266-B435-11E9-9278-68D0E5697425
grant_number: EP-P026710-2
name: Between rational and integral points
publication: Algebra and Number Theory
publication_identifier:
eissn:
- 1944-7833
issn:
- 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Free rational curves on low degree hypersurfaces and the circle method
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: 17
year: '2023'
...
---
_id: '13180'
abstract:
- lang: eng
text: We study the density of everywhere locally soluble diagonal quadric surfaces,
parameterised by rational points that lie on a split quadric surface
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: Julian
full_name: Lyczak, Julian
id: 3572849A-F248-11E8-B48F-1D18A9856A87
last_name: Lyczak
- first_name: Roman
full_name: Sarapin, Roman
last_name: Sarapin
citation:
ama: Browning TD, Lyczak J, Sarapin R. Local solubility for a family of quadrics
over a split quadric surface. Involve. 2023;16(2):331-342. doi:10.2140/involve.2023.16.331
apa: Browning, T. D., Lyczak, J., & Sarapin, R. (2023). Local solubility for
a family of quadrics over a split quadric surface. Involve. Mathematical
Sciences Publishers. https://doi.org/10.2140/involve.2023.16.331
chicago: Browning, Timothy D, Julian Lyczak, and Roman Sarapin. “Local Solubility
for a Family of Quadrics over a Split Quadric Surface.” Involve. Mathematical
Sciences Publishers, 2023. https://doi.org/10.2140/involve.2023.16.331.
ieee: T. D. Browning, J. Lyczak, and R. Sarapin, “Local solubility for a family
of quadrics over a split quadric surface,” Involve, vol. 16, no. 2. Mathematical
Sciences Publishers, pp. 331–342, 2023.
ista: Browning TD, Lyczak J, Sarapin R. 2023. Local solubility for a family of quadrics
over a split quadric surface. Involve. 16(2), 331–342.
mla: Browning, Timothy D., et al. “Local Solubility for a Family of Quadrics over
a Split Quadric Surface.” Involve, vol. 16, no. 2, Mathematical Sciences
Publishers, 2023, pp. 331–42, doi:10.2140/involve.2023.16.331.
short: T.D. Browning, J. Lyczak, R. Sarapin, Involve 16 (2023) 331–342.
corr_author: '1'
date_created: 2023-07-02T22:00:43Z
date_published: 2023-05-26T00:00:00Z
date_updated: 2024-10-09T21:05:51Z
day: '26'
department:
- _id: TiBr
doi: 10.2140/involve.2023.16.331
external_id:
arxiv:
- '2203.06881'
intvolume: ' 16'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2203.06881
month: '05'
oa: 1
oa_version: Preprint
page: 331-342
publication: Involve
publication_identifier:
eissn:
- 1944-4184
issn:
- 1944-4176
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local solubility for a family of quadrics over a split quadric surface
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16
year: '2023'
...
---
_id: '8682'
abstract:
- lang: eng
text: It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous
for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover,
for such varieties it follows from a general conjecture of Colliot-Thélène that
the Brauer--Manin obstruction to the Hasse principle should be the only one, so
that the Hasse principle is expected to hold. Working over the field of rational
numbers and ordering Fano hypersurfaces of fixed degree and dimension by height,
we prove that almost every such hypersurface satisfies the Hasse principle provided
that the dimension is at least 3. This proves a conjecture of Poonen and Voloch
in every case except for cubic surfaces.
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: Pierre Le
full_name: Boudec, Pierre Le
last_name: Boudec
- first_name: Will
full_name: Sawin, Will
last_name: Sawin
citation:
ama: Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces.
Annals of Mathematics. 2023;197(3):1115-1203. doi:10.4007/annals.2023.197.3.3
apa: Browning, T. D., Boudec, P. L., & Sawin, W. (2023). The Hasse principle
for random Fano hypersurfaces. Annals of Mathematics. Princeton University.
https://doi.org/10.4007/annals.2023.197.3.3
chicago: Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle
for Random Fano Hypersurfaces.” Annals of Mathematics. Princeton University,
2023. https://doi.org/10.4007/annals.2023.197.3.3.
ieee: T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random
Fano hypersurfaces,” Annals of Mathematics, vol. 197, no. 3. Princeton
University, pp. 1115–1203, 2023.
ista: Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano
hypersurfaces. Annals of Mathematics. 197(3), 1115–1203.
mla: Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.”
Annals of Mathematics, vol. 197, no. 3, Princeton University, 2023, pp.
1115–203, doi:10.4007/annals.2023.197.3.3.
short: T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203.
corr_author: '1'
date_created: 2020-10-19T14:28:50Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2024-10-21T06:01:30Z
day: '01'
department:
- _id: TiBr
doi: 10.4007/annals.2023.197.3.3
external_id:
arxiv:
- '2006.02356'
isi:
- '000966611000003'
intvolume: ' 197'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2006.02356
month: '05'
oa: 1
oa_version: Preprint
page: 1115-1203
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Princeton University
quality_controlled: '1'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/when-is-necessary-sufficient/
scopus_import: '1'
status: public
title: The Hasse principle for random Fano hypersurfaces
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 197
year: '2023'
...
---
_id: '12776'
abstract:
- lang: eng
text: An improved asymptotic formula is established for the number of rational points
of bounded height on the split smooth del Pezzo surface of degree 5. The proof
uses the five conic bundle structures on the surface.
acknowledgement: This work was begun while the author was participating in the programme
on "Diophantine equations" at the Hausdorff Research Institute for Mathematics in
Bonn in 2009. The hospitality and financial support of the institute is gratefully
acknowledged. The idea of using conic bundles to study the split del Pezzo surface
of degree 5 was explained to the author by Professor Salberger. The author is very
grateful to him for his input into this project and also to Shuntaro Yamagishi for
many useful comments on an earlier version of this manuscript. While working on
this paper the author was supported by FWF grant P32428-N35.
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
citation:
ama: Browning TD. Revisiting the Manin–Peyre conjecture for the split del Pezzo
surface of degree 5. New York Journal of Mathematics. 2022;28:1193-1229.
apa: Browning, T. D. (2022). Revisiting the Manin–Peyre conjecture for the split
del Pezzo surface of degree 5. New York Journal of Mathematics. State University
of New York.
chicago: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split
Del Pezzo Surface of Degree 5.” New York Journal of Mathematics. State
University of New York, 2022.
ieee: T. D. Browning, “Revisiting the Manin–Peyre conjecture for the split del Pezzo
surface of degree 5,” New York Journal of Mathematics, vol. 28. State University
of New York, pp. 1193–1229, 2022.
ista: Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del
Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229.
mla: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del
Pezzo Surface of Degree 5.” New York Journal of Mathematics, vol. 28, State
University of New York, 2022, pp. 1193–229.
short: T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229.
corr_author: '1'
date_created: 2023-03-28T09:21:09Z
date_published: 2022-08-24T00:00:00Z
date_updated: 2025-04-15T07:39:01Z
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publication: New York Journal of Mathematics
publication_identifier:
issn:
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publication_status: published
publisher: State University of New York
quality_controlled: '1'
status: public
title: Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree
5
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abstract:
- lang: eng
text: "We associate a certain tensor product lattice to any primitive integer lattice
and ask about its typical shape. These lattices are related to the tangent bundle
of Grassmannians and their study is motivated by Peyre's programme on \"freeness\"
for rational points of bounded height on Fano\r\nvarieties."
acknowledgement: The authors are very grateful to Will Sawin for useful remarks about
this topic. While working on this paper the first two authors were supported by
EPSRC grant EP/P026710/1, and the first and last authors by FWF grant P 32428-N35.
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author:
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full_name: Browning, Timothy D
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last_name: Browning
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- first_name: Tal
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- first_name: Florian Alexander
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ama: Browning TD, Horesh T, Wilsch FA. Equidistribution and freeness on Grassmannians.
Algebra & Number Theory. 2022;16(10):2385-2407. doi:10.2140/ant.2022.16.2385
apa: Browning, T. D., Horesh, T., & Wilsch, F. A. (2022). Equidistribution and
freeness on Grassmannians. Algebra & Number Theory. Mathematical Sciences
Publishers. https://doi.org/10.2140/ant.2022.16.2385
chicago: Browning, Timothy D, Tal Horesh, and Florian Alexander Wilsch. “Equidistribution
and Freeness on Grassmannians.” Algebra & Number Theory. Mathematical
Sciences Publishers, 2022. https://doi.org/10.2140/ant.2022.16.2385.
ieee: T. D. Browning, T. Horesh, and F. A. Wilsch, “Equidistribution and freeness
on Grassmannians,” Algebra & Number Theory, vol. 16, no. 10. Mathematical
Sciences Publishers, pp. 2385–2407, 2022.
ista: Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians.
Algebra & Number Theory. 16(10), 2385–2407.
mla: Browning, Timothy D., et al. “Equidistribution and Freeness on Grassmannians.”
Algebra & Number Theory, vol. 16, no. 10, Mathematical Sciences Publishers,
2022, pp. 2385–407, doi:10.2140/ant.2022.16.2385.
short: T.D. Browning, T. Horesh, F.A. Wilsch, Algebra & Number Theory 16 (2022)
2385–2407.
corr_author: '1'
date_created: 2021-02-25T09:56:57Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2025-04-14T09:25:44Z
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department:
- _id: TiBr
doi: 10.2140/ant.2022.16.2385
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...
---
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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:
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full_name: Browning, Timothy D
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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.
corr_author: '1'
date_created: 2021-12-05T23:01:46Z
date_published: 2021-12-01T00:00:00Z
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publisher: Springer Nature
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title: Cubic Forms and the Circle Method
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...