---
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
content_type: application/pdf
creator: dernst
date_created: 2026-01-19T08:19:46Z
date_updated: 2026-01-19T08:19:46Z
file_id: '21004'
file_name: 2026_JourLondonMathSoc_Browning.pdf
file_size: 235238
relation: main_file
success: 1
file_date_updated: 2026-01-19T08:19:46Z
has_accepted_license: '1'
intvolume: ' 113'
issue: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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
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: 113
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '21242'
abstract:
- lang: eng
text: We obtain an asymptotic formula for the number of integral solutions to a
system of diagonal equations. We obtain an asymptotic formula for the number of
solutions with variables restricted to smooth numbers as well. We improve the
required number of variables compared to previous results by incorporating recent
progress on Waring’s problem and the resolution of the main conjecture in Vinogradov’s
mean value theorem.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nick
full_name: Rome, Nick
last_name: Rome
- first_name: Shuntaro
full_name: Yamagishi, Shuntaro
id: 0c3fbc5c-f7a6-11ec-8d70-9485e75b416b
last_name: Yamagishi
citation:
ama: Rome N, Yamagishi S. Integral solutions to systems of diagonal equations. Pacific
Journal of Mathematics. 2026;340(1):179-198. doi:10.2140/pjm.2026.340.179
apa: Rome, N., & Yamagishi, S. (2026). Integral solutions to systems of diagonal
equations. Pacific Journal of Mathematics. Mathematical Sciences Publishers.
https://doi.org/10.2140/pjm.2026.340.179
chicago: Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal
Equations.” Pacific Journal of Mathematics. Mathematical Sciences Publishers,
2026. https://doi.org/10.2140/pjm.2026.340.179.
ieee: N. Rome and S. Yamagishi, “Integral solutions to systems of diagonal equations,”
Pacific Journal of Mathematics, vol. 340, no. 1. Mathematical Sciences
Publishers, pp. 179–198, 2026.
ista: Rome N, Yamagishi S. 2026. Integral solutions to systems of diagonal equations.
Pacific Journal of Mathematics. 340(1), 179–198.
mla: Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal
Equations.” Pacific Journal of Mathematics, vol. 340, no. 1, Mathematical
Sciences Publishers, 2026, pp. 179–98, doi:10.2140/pjm.2026.340.179.
short: N. Rome, S. Yamagishi, Pacific Journal of Mathematics 340 (2026) 179–198.
date_created: 2026-02-16T15:17:27Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-02-17T11:43:14Z
day: '01'
department:
- _id: TiBr
doi: 10.2140/pjm.2026.340.179
external_id:
arxiv:
- '2406.09256'
intvolume: ' 340'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2406.09256
month: '01'
oa: 1
oa_version: Preprint
page: 179-198
publication: Pacific Journal of Mathematics
publication_identifier:
eissn:
- 1945-5844
issn:
- 0030-8730
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
status: public
title: Integral solutions to systems of diagonal equations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 340
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21385'
abstract:
- lang: eng
text: 'We prove that the average size of a mixed character sum (math. formular)
(for a suitable smooth function w) is on the order of √x for all irrational real
θ satisfying a weak Diophantine condition, where χ is drawn from the family of
Dirichlet characters modulo a large prime r and where x 6 r. In contrast, it was
proved by Harper that the average size is o(√x) for rational θ. Certain quadratic
Diophantine equations play a key role in the present paper. '
acknowledgement: "We thank Ofir Gorodetsky, Andrew Granville, Adam Harper, Youness
Lamzouri,\r\nKannan Soundararajan, Ping Xi, and Matt Young for their interest, helpful
discussions, and comments. Special thanks are due to Jonathan Bober, Oleksiy Klurman,\r\nand
Besfort Shala for sending us a letter about Question 1.3, and to Hung Bui\r\nfor
informing us of [7]. V.W. thanks Stanford University for its hospitality and is
supported by the European Union’s Horizon 2020 research and innovation program\r\nunder
the Marie Skłodowska–Curie Grant Agreement No. 101034413. M.X. is supported by a
Simons Junior Fellowship from the Simons Society of Fellows at the\r\nSimons Foundation."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Victor
full_name: Wang, Victor
id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
last_name: Wang
orcid: 0000-0002-0704-7026
- first_name: Max
full_name: Xu, Max
last_name: Xu
citation:
ama: 'Wang V, Xu M. Average sizes of mixed character sums. Proceedings of the
Royal Society of Edinburgh: Section A Mathematics. 2026:1-15. doi:10.1017/prm.2026.10123'
apa: 'Wang, V., & Xu, M. (2026). Average sizes of mixed character sums. Proceedings
of the Royal Society of Edinburgh: Section A Mathematics. Cambridge University
Press. https://doi.org/10.1017/prm.2026.10123'
chicago: 'Wang, Victor, and Max Xu. “Average Sizes of Mixed Character Sums.” Proceedings
of the Royal Society of Edinburgh: Section A Mathematics. Cambridge University
Press, 2026. https://doi.org/10.1017/prm.2026.10123.'
ieee: 'V. Wang and M. Xu, “Average sizes of mixed character sums,” Proceedings
of the Royal Society of Edinburgh: Section A Mathematics. Cambridge University
Press, pp. 1–15, 2026.'
ista: 'Wang V, Xu M. 2026. Average sizes of mixed character sums. Proceedings of
the Royal Society of Edinburgh: Section A Mathematics., 1–15.'
mla: 'Wang, Victor, and Max Xu. “Average Sizes of Mixed Character Sums.” Proceedings
of the Royal Society of Edinburgh: Section A Mathematics, Cambridge University
Press, 2026, pp. 1–15, doi:10.1017/prm.2026.10123.'
short: 'V. Wang, M. Xu, Proceedings of the Royal Society of Edinburgh: Section A
Mathematics (2026) 1–15.'
corr_author: '1'
date_created: 2026-03-02T10:09:23Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-03-02T14:05:47Z
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/prm.2026.10123
ec_funded: 1
external_id:
arxiv:
- '2411.14181'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1017/prm.2026.10123
month: '01'
oa: 1
oa_version: Published Version
page: 1-15
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: 'Proceedings of the Royal Society of Edinburgh: Section A Mathematics'
publication_identifier:
eissn:
- 1473-7124
issn:
- 0308-2105
publication_status: epub_ahead
publisher: Cambridge University Press
quality_controlled: '1'
status: public
title: Average sizes of mixed character sums
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
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18705'
abstract:
- lang: eng
text: Given a non-singular diagonal cubic hypersurface X⊂Pn−1 over Fq(t) with char(Fq)≠3,
we show that the number of rational points of height at most |P| is O(|P|3+ε)
for n=6 and O(|P|2+ε) for n=4. In fact, if n=4 and char(Fq)>3 we prove that the
number of rational points away from any rational line contained in X is bounded
by O(|P|3/2+ε). From the result in 6 variables we deduce weak approximation for
diagonal cubic hypersurfaces for n≥7 over Fq(t) when char(Fq)>3 and handle Waring's
problem for cubes in 7 variables over Fq(t) when char(Fq)≠3. Our results answer
a question of Davenport regarding the number of solutions of bounded height to
x31+x32+x33=x34+x35+x36 with xi∈Fq[t].
acknowledgement: "Open Access funding enabled and organized by Projekt DEAL.\r\nThe
authors would like to thank Tim Browning for suggesting this project. Further they
are grateful for his and Damaris Schindler’s helpful comments. We would also like
to thank Efthymios Sofos for bringing Davenport’s question to our attention and
Keith Matthews for providing us with scanned copies of the original correspondence.
Finally we would like to thank the reviewer for helpful comments."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jakob
full_name: Glas, Jakob
id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb
last_name: Glas
- first_name: Leonhard
full_name: Hochfilzer, Leonhard
last_name: Hochfilzer
citation:
ama: Glas J, Hochfilzer L. On a question of Davenport and diagonal cubic forms over
Fq(t). Mathematische Annalen. 2025;391:5485-5533. doi:10.1007/s00208-024-03035-z
apa: Glas, J., & Hochfilzer, L. (2025). On a question of Davenport and diagonal
cubic forms over Fq(t). Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-024-03035-z
chicago: Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal
Cubic Forms over Fq(T).” Mathematische Annalen. Springer Nature, 2025.
https://doi.org/10.1007/s00208-024-03035-z.
ieee: J. Glas and L. Hochfilzer, “On a question of Davenport and diagonal cubic
forms over Fq(t),” Mathematische Annalen, vol. 391. Springer Nature, pp.
5485–5533, 2025.
ista: Glas J, Hochfilzer L. 2025. On a question of Davenport and diagonal cubic
forms over Fq(t). Mathematische Annalen. 391, 5485–5533.
mla: Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal
Cubic Forms over Fq(T).” Mathematische Annalen, vol. 391, Springer Nature,
2025, pp. 5485–533, doi:10.1007/s00208-024-03035-z.
short: J. Glas, L. Hochfilzer, Mathematische Annalen 391 (2025) 5485–5533.
corr_author: '1'
date_created: 2024-12-22T23:01:48Z
date_published: 2025-04-01T00:00:00Z
date_updated: 2025-05-19T14:04:46Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s00208-024-03035-z
external_id:
arxiv:
- '2208.05422'
isi:
- '001376740400001'
file:
- access_level: open_access
checksum: dcf57a8b01332c36e0cf2b0d1aeecb36
content_type: application/pdf
creator: dernst
date_created: 2025-04-16T09:38:55Z
date_updated: 2025-04-16T09:38:55Z
file_id: '19579'
file_name: 2025_MathAnnalen_Glas.pdf
file_size: 650021
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success: 1
file_date_updated: 2025-04-16T09:38:55Z
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intvolume: ' 391'
isi: 1
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 5485-5533
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '18293'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: On a question of Davenport and diagonal cubic forms over 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 391
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '12311'
abstract:
- lang: eng
text: In this note, we prove a formula for the cancellation exponent kv,n between
division polynomials ψn and ϕn associated with a sequence {nP}n∈N of points
on an elliptic curve E defined over a discrete valuation field K. The formula
greatly generalizes the previously known special cases and treats also the case
of non-standard Kodaira types for non-perfect residue fields.
acknowledgement: Silverman, and Paul Voutier for the comments on the earlier version
of this paper. The first author acknowledges the support by Dioscuri programme initiated
by the Max Planck Society, jointly managed with the National Science Centre (Poland),
and mutually funded by the Polish Ministry of Science and Higher Education and the
German Federal Ministry of Education and Research. The second author has been supported
by MIUR (Italy) through PRIN 2017 ‘Geometric, algebraic and analytic methods in
arithmetic’ and has received funding from the European Union's Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Bartosz
full_name: Naskręcki, Bartosz
last_name: Naskręcki
- first_name: Matteo
full_name: Verzobio, Matteo
id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
last_name: Verzobio
orcid: 0000-0002-0854-0306
citation:
ama: 'Naskręcki B, Verzobio M. Common valuations of division polynomials. Proceedings
of the Royal Society of Edinburgh Section A: Mathematics. 2025;155(5):1646-1660.
doi:10.1017/prm.2024.7'
apa: 'Naskręcki, B., & Verzobio, M. (2025). Common valuations of division polynomials.
Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Cambridge
University Press. https://doi.org/10.1017/prm.2024.7'
chicago: 'Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division
Polynomials.” Proceedings of the Royal Society of Edinburgh Section A: Mathematics.
Cambridge University Press, 2025. https://doi.org/10.1017/prm.2024.7.'
ieee: 'B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,”
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol.
155, no. 5. Cambridge University Press, pp. 1646–1660, 2025.'
ista: 'Naskręcki B, Verzobio M. 2025. Common valuations of division polynomials.
Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 155(5),
1646–1660.'
mla: 'Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.”
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol.
155, no. 5, Cambridge University Press, 2025, pp. 1646–60, doi:10.1017/prm.2024.7.'
short: 'B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh
Section A: Mathematics 155 (2025) 1646–1660.'
corr_author: '1'
date_created: 2023-01-16T11:45:22Z
date_published: 2025-10-01T00:00:00Z
date_updated: 2025-12-30T06:46:17Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/prm.2024.7
ec_funded: 1
external_id:
arxiv:
- '2203.02015'
isi:
- '001174907100001'
file:
- access_level: open_access
checksum: c5ec6e29aca2fb4533cb95fac409a0b2
content_type: application/pdf
creator: dernst
date_created: 2025-12-30T06:45:47Z
date_updated: 2025-12-30T06:45:47Z
file_id: '20878'
file_name: 2025_ProceedingsRoyalSocEdinburghA_Naskrecki.pdf
file_size: 477624
relation: main_file
success: 1
file_date_updated: 2025-12-30T06:45:47Z
has_accepted_license: '1'
intvolume: ' 155'
isi: 1
issue: '5'
keyword:
- Elliptic curves
- Néron models
- division polynomials
- height functions
- discrete valuation rings
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1646-1660
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: 'Proceedings of the Royal Society of Edinburgh Section A: Mathematics'
publication_identifier:
eissn:
- 1473-7124
issn:
- 0308-2105
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Common valuations of division 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 155
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20078'
abstract:
- lang: eng
text: 'Let A be an abelian variety defined over a number field K, E/K be an elliptic
curve, and ϕ : A → Em be an isogeny defined over K. Let P ∈ A(K) be such that
ϕ(P)=(Q1,..., Qm) with RankZ(⟨Q1,...,Qm⟩)=1. We will study a divisibility sequence
related to the point P and show its relation with elliptic divisibility sequences.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Stefan
full_name: Barańczuk, Stefan
last_name: Barańczuk
- first_name: Bartosz
full_name: Naskręcki, Bartosz
last_name: Naskręcki
- first_name: Matteo
full_name: Verzobio, Matteo
id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
last_name: Verzobio
orcid: 0000-0002-0854-0306
citation:
ama: Barańczuk S, Naskręcki B, Verzobio M. Divisibility sequences related to abelian
varieties isogenous to a power of an elliptic curve. Journal of Number Theory.
2025;279:170-183. doi:10.1016/j.jnt.2025.06.001
apa: Barańczuk, S., Naskręcki, B., & Verzobio, M. (2025). Divisibility sequences
related to abelian varieties isogenous to a power of an elliptic curve. Journal
of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2025.06.001
chicago: Barańczuk, Stefan, Bartosz Naskręcki, and Matteo Verzobio. “Divisibility
Sequences Related to Abelian Varieties Isogenous to a Power of an Elliptic Curve.”
Journal of Number Theory. Elsevier, 2025. https://doi.org/10.1016/j.jnt.2025.06.001.
ieee: S. Barańczuk, B. Naskręcki, and M. Verzobio, “Divisibility sequences related
to abelian varieties isogenous to a power of an elliptic curve,” Journal of
Number Theory, vol. 279. Elsevier, pp. 170–183, 2025.
ista: Barańczuk S, Naskręcki B, Verzobio M. 2025. Divisibility sequences related
to abelian varieties isogenous to a power of an elliptic curve. Journal of Number
Theory. 279, 170–183.
mla: Barańczuk, Stefan, et al. “Divisibility Sequences Related to Abelian Varieties
Isogenous to a Power of an Elliptic Curve.” Journal of Number Theory, vol.
279, Elsevier, 2025, pp. 170–83, doi:10.1016/j.jnt.2025.06.001.
short: S. Barańczuk, B. Naskręcki, M. Verzobio, Journal of Number Theory 279 (2025)
170–183.
corr_author: '1'
date_created: 2025-07-27T22:01:25Z
date_published: 2025-07-23T00:00:00Z
date_updated: 2025-09-30T14:09:38Z
day: '23'
department:
- _id: TiBr
doi: 10.1016/j.jnt.2025.06.001
external_id:
arxiv:
- '2309.09699'
isi:
- '001541172400002'
intvolume: ' 279'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.jnt.2025.06.001
month: '07'
oa: 1
oa_version: Published Version
page: 170-183
publication: Journal of Number Theory
publication_identifier:
issn:
- 0022-314X
publication_status: epub_ahead
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Divisibility sequences related to abelian varieties isogenous to a power of
an elliptic curve
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 279
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '20222'
abstract:
- lang: eng
text: Let X be a smooth projective hypersurface defined over Q. We provide new bounds
for rational points of bounded height on X. In particular, we show that if X is
a smooth projective hypersurface in Pn with n 4 and degree d 50, then the set
of rational points on X of height bounded by B have cardinality On,d,ε (Bn−2+ε
). If X is smooth and has degree d 6, we improve the dimension growth conjecture
bound. We achieve an analogue result for affine hypersurfaces whose projective
closure is smooth.
acknowledgement: "While working on this paper, the author was supported by the European
Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie
Grant Agreement No. 101034413. The author is very grateful to Tim Browning for suggesting
the problem and for many useful discussions. We thank the anonymous referees for
their many helpful comments, which improved the exposition of the paper. We are
also grateful to Gal Binyamini for their interest in this work and for drawing our
attention to the aforementioned paper [1].\r\nWe shared an early version of this
paper with Per Salberger, who mentioned that he announced a new bound for smooth
threefolds in P4 during a talk in 2019 (see [7] for the abstract). This result has
not been published."
article_number: rnaf249
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matteo
full_name: Verzobio, Matteo
id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
last_name: Verzobio
orcid: 0000-0002-0854-0306
citation:
ama: Verzobio M. Counting rational points on smooth hypersurfaces with high degree.
International Mathematics Research Notices. 2025;2025(16). doi:10.1093/imrn/rnaf249
apa: Verzobio, M. (2025). Counting rational points on smooth hypersurfaces with
high degree. International Mathematics Research Notices. Oxford University
Press. https://doi.org/10.1093/imrn/rnaf249
chicago: Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with
High Degree.” International Mathematics Research Notices. Oxford University
Press, 2025. https://doi.org/10.1093/imrn/rnaf249.
ieee: M. Verzobio, “Counting rational points on smooth hypersurfaces with high degree,”
International Mathematics Research Notices, vol. 2025, no. 16. Oxford University
Press, 2025.
ista: Verzobio M. 2025. Counting rational points on smooth hypersurfaces with high
degree. International Mathematics Research Notices. 2025(16), rnaf249.
mla: Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with High
Degree.” International Mathematics Research Notices, vol. 2025, no. 16,
rnaf249, Oxford University Press, 2025, doi:10.1093/imrn/rnaf249.
short: M. Verzobio, International Mathematics Research Notices 2025 (2025).
corr_author: '1'
date_created: 2025-08-24T22:01:31Z
date_published: 2025-08-01T00:00:00Z
date_updated: 2025-09-30T14:26:34Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1093/imrn/rnaf249
ec_funded: 1
external_id:
arxiv:
- '2503.19451'
isi:
- '001549126000001'
file:
- access_level: open_access
checksum: 482ae2be98841ee446cf2bdfcd79f86f
content_type: application/pdf
creator: dernst
date_created: 2025-09-02T07:55:05Z
date_updated: 2025-09-02T07:55:05Z
file_id: '20275'
file_name: 2025_IMRN_Verzobio.pdf
file_size: 540263
relation: main_file
success: 1
file_date_updated: 2025-09-02T07:55:05Z
has_accepted_license: '1'
intvolume: ' 2025'
isi: 1
issue: '16'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting rational points on smooth hypersurfaces with high degree
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 2025
year: '2025'
...
---
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
PlanS_conform: '1'
_id: '20423'
abstract:
- lang: eng
text: "For any d 2, we prove that there exists an integer n0(d) such that there
exists an n × n\r\nmagic square of dth powers for all n n0(d). In particular,
we establish the existence of\r\nan n × n magic square of squares for all n 4,
which settles a conjecture of\r\nVárilly-Alvarado. All previous approaches had
been based on constructive methods and\r\nthe existence of n × n magic squares
of dth powers had only been known for sparse\r\nvalues of n. We prove our result
by the Hardy-Littlewood circle method, which in this\r\nsetting essentially reduces
the problem to finding a sufficient number of disjoint linearly\r\nindependent
subsets of the columns of the coefficient matrix of the equations defining\r\nmagic
squares. We prove an optimal (up to a constant) lower bound for this quantity."
acknowledgement: "The authors are grateful to Tim Browning for his constant encouragement
and enthusiasm, Jörg Brüdern for very helpful discussion regarding his paper [1]
and Diyuan Wu for turning the proof of Theorem 2.4 in the original version into
an algorithm and running the computation for us, for which the results are available
in the appendix of the original version. They would also like to thank Christian
Boyer for maintaining his website [4] which contains a comprehensive list of various
magic squares discovered, Brady Haran and Tony Várilly-Alvarado for their public
engagement activity of mathematics and magic squares of squares (A YouTube video
“Magic Squares of Squares (are PROBABLY impossible)” of the Numberphile channel
by Brady Haran, in which Tony Várilly-Alvarado appears as a guest speaker: https://www.youtube.com/watch?v=Kdsj84UdeYg.),
and all the magic squares enthusiasts who have contributed to [4] which made this
paper possible. Finally, the authors would like to thank the anonymous referees
for their helpful comments, Daniel Flores for his work [11] which inspired them
to optimise the proof of Theorem 2.4 and Trevor Wooley for very helpful discussion
regarding recent developments in Waring’s problem and his comments on the original
version of this paper.\r\nOpen access funding provided by Institute of Science and
Technology (IST Austria). NR was supported by FWF project ESP 441-NBL while SY by
a FWF grant (DOI 10.55776/P32428)."
article_number: '91'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Nick
full_name: Rome, Nick
last_name: Rome
- first_name: Shuntaro
full_name: Yamagishi, Shuntaro
id: 0c3fbc5c-f7a6-11ec-8d70-9485e75b416b
last_name: Yamagishi
citation:
ama: Rome N, Yamagishi S. On the existence of magic squares of powers. Research
in Number Theory. 2025;11(4). doi:10.1007/s40993-025-00671-5
apa: Rome, N., & Yamagishi, S. (2025). On the existence of magic squares of
powers. Research in Number Theory. Springer Nature. https://doi.org/10.1007/s40993-025-00671-5
chicago: Rome, Nick, and Shuntaro Yamagishi. “On the Existence of Magic Squares
of Powers.” Research in Number Theory. Springer Nature, 2025. https://doi.org/10.1007/s40993-025-00671-5.
ieee: N. Rome and S. Yamagishi, “On the existence of magic squares of powers,” Research
in Number Theory, vol. 11, no. 4. Springer Nature, 2025.
ista: Rome N, Yamagishi S. 2025. On the existence of magic squares of powers. Research
in Number Theory. 11(4), 91.
mla: Rome, Nick, and Shuntaro Yamagishi. “On the Existence of Magic Squares of Powers.”
Research in Number Theory, vol. 11, no. 4, 91, Springer Nature, 2025, doi:10.1007/s40993-025-00671-5.
short: N. Rome, S. Yamagishi, Research in Number Theory 11 (2025).
corr_author: '1'
date_created: 2025-10-05T22:01:34Z
date_published: 2025-09-23T00:00:00Z
date_updated: 2025-10-13T12:30:40Z
day: '23'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1007/s40993-025-00671-5
external_id:
arxiv:
- '2406.09364'
file:
- access_level: open_access
checksum: d41fbdc0cfc1fbceb519eb49b20a3ec2
content_type: application/pdf
creator: dernst
date_created: 2025-10-13T11:28:49Z
date_updated: 2025-10-13T11:28:49Z
file_id: '20463'
file_name: 2025_ResearchNumberTheory_Rome.pdf
file_size: 428531
relation: main_file
success: 1
file_date_updated: 2025-10-13T11:28:49Z
has_accepted_license: '1'
intvolume: ' 11'
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
publication: Research in Number Theory
publication_identifier:
eissn:
- 2363-9555
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the existence of magic squares of powers
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: 11
year: '2025'
...
---
OA_type: closed access
_id: '20603'
abstract:
- lang: eng
text: "We study the growth of sumsets A+B⊂S⊂G, where S does not contain an arithmetic
progression of length 2k+1, and where G is a commutative group, in which every
nonzero element has an order of at least 2k+1. More specifically, we show the
following: if A,B⊂G are sets such that A+B does not contain an arithmetic progression
of length 2k+1, then\r\n|A+B|≥|A|2k−13k−2|B|k3k−2.\r\nAs an application we derive
upper bounds on the cardinality of the summands in sumsets A+B+C contained in
the set of t-th powers, where t≥2 is an integer. In particular, we show that min(|A|,|B|,|C|)≪(logN)4/5
for t=2, and min(|A|,|B|,|C|)≪t(logN)1/2 for t≥3."
acknowledgement: "The authors would like to thank the referee and Ilya Shkredov for
comments on the manuscript.\r\nC. E. is supported by a joint FWF-ANR project ArithRand,
grant numbers FWF I 4945-N and ANR-20-CE91-0006.\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Christian
full_name: Elsholtz, Christian
last_name: Elsholtz
- first_name: Imre Z.
full_name: Ruzsa, Imre Z.
last_name: Ruzsa
- first_name: Lena
full_name: Wurzinger, Lena
id: 50c57d72-32a8-11ee-aeea-d652094d2ccd
last_name: Wurzinger
orcid: 0009-0004-5360-0074
citation:
ama: Elsholtz C, Ruzsa IZ, Wurzinger L. Sumset growth in progression-free sets.
Acta Arithmetica. 2025;220:289-303. doi:10.4064/aa250115-14-7
apa: Elsholtz, C., Ruzsa, I. Z., & Wurzinger, L. (2025). Sumset growth in progression-free
sets. Acta Arithmetica. Institute of Mathematics. https://doi.org/10.4064/aa250115-14-7
chicago: Elsholtz, Christian, Imre Z. Ruzsa, and Lena Wurzinger. “Sumset Growth
in Progression-Free Sets.” Acta Arithmetica. Institute of Mathematics,
2025. https://doi.org/10.4064/aa250115-14-7.
ieee: C. Elsholtz, I. Z. Ruzsa, and L. Wurzinger, “Sumset growth in progression-free
sets,” Acta Arithmetica, vol. 220. Institute of Mathematics, pp. 289–303,
2025.
ista: Elsholtz C, Ruzsa IZ, Wurzinger L. 2025. Sumset growth in progression-free
sets. Acta Arithmetica. 220, 289–303.
mla: Elsholtz, Christian, et al. “Sumset Growth in Progression-Free Sets.” Acta
Arithmetica, vol. 220, Institute of Mathematics, 2025, pp. 289–303, doi:10.4064/aa250115-14-7.
short: C. Elsholtz, I.Z. Ruzsa, L. Wurzinger, Acta Arithmetica 220 (2025) 289–303.
corr_author: '1'
date_created: 2025-11-04T14:33:16Z
date_published: 2025-09-12T00:00:00Z
date_updated: 2025-12-01T15:18:09Z
day: '12'
department:
- _id: TiBr
doi: 10.4064/aa250115-14-7
external_id:
isi:
- '001570716800001'
intvolume: ' 220'
isi: 1
language:
- iso: eng
month: '09'
oa_version: None
page: 289-303
publication: Acta Arithmetica
publication_identifier:
eissn:
- 1730-6264
issn:
- 0065-1036
publication_status: published
publisher: Institute of Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sumset growth in progression-free sets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 220
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18822'
abstract:
- lang: eng
text: Let N(X) be the number of integral zeros (mathematical equation). Works of
Hooley and Heath-Brown imply (mathematical equation), if one assumes automorphy
and grand Riemann hypothesis for certain Hasse–Weil L-functions. Assuming instead
a natural large sieve inequality, we recover the same bound on N(X). This is part
of a more general statement, for diagonal cubic forms in (mathematical equation)
variables, where we allow approximations to Hasse–Weil L-functions.
acknowledgement: I thank Peter Sarnak for suggesting projects that ultimately led
to the present paper. I also thank him for many encouraging discussions, helpful
comments, and references. Thanks also to Tim Browning, Trevor Wooley, and Nina Zubrilina
for helpful comments, and to Levent Alpöge and Will Sawin for some interesting old
discussions. I thank Yang Liu, Evan O'Dorney, Ashwin Sah, and Mark Sellke for conversations
illuminating the combinatorics of an older, counting version of the present Lemma
4.9. Finally, special thanks are due to the editors and referees for their patience
and help with the exposition. This work was partially supported by NSF Grant DMS-1802211,
and the European Union's Horizon 2020 research and innovation program under the
Marie Skłodowska-Curie Grant Agreement No. 101034413.
article_number: e70008
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Victor
full_name: Wang, Victor
id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
last_name: Wang
orcid: 0000-0002-0704-7026
citation:
ama: Wang V. Diagonal cubic forms and the large sieve. Mathematika. 2025;71(1).
doi:10.1112/mtk.70008
apa: Wang, V. (2025). Diagonal cubic forms and the large sieve. Mathematika.
London Mathematical Society. https://doi.org/10.1112/mtk.70008
chicago: Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” Mathematika.
London Mathematical Society, 2025. https://doi.org/10.1112/mtk.70008.
ieee: V. Wang, “Diagonal cubic forms and the large sieve,” Mathematika, vol.
71, no. 1. London Mathematical Society, 2025.
ista: Wang V. 2025. Diagonal cubic forms and the large sieve. Mathematika. 71(1),
e70008.
mla: Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” Mathematika,
vol. 71, no. 1, e70008, London Mathematical Society, 2025, doi:10.1112/mtk.70008.
short: V. Wang, Mathematika 71 (2025).
corr_author: '1'
date_created: 2025-01-12T23:04:01Z
date_published: 2025-01-02T00:00:00Z
date_updated: 2025-04-14T07:54:56Z
day: '02'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1112/mtk.70008
ec_funded: 1
external_id:
isi:
- '001388255500001'
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checksum: 700a8596b4bffce2320d074120962c22
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relation: main_file
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intvolume: ' 71'
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month: '01'
oa: 1
oa_version: Published Version
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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: Diagonal cubic forms and the large sieve
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 71
year: '2025'
...
---
OA_place: publisher
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abstract:
- lang: eng
text: "This work concerns asymptotical stabilisation phenomena occurring in the
moduli space of sections of certain algebraic families over a smooth projective
curve, whenever the generic fibre of the family is a smooth projective Fano variety,
or not far from being Fano.\r\n We describe the expected behaviour of the class,
in a ring of motivic integration, of the moduli space of sections of given numerical
class. Up to an adequate normalisation, it should converge, when the class of
the sections goes arbitrarily far from the boundary of the dual of the effective
cone, to an effective element given by a motivic Euler product. Such a principle
can be seen as an analogue for rational curves of the Batyrev-Manin-Peyre principle
for rational points.\r\n The central tool of this article is the property of equidistribution
of curves. We show that this notion does not depend on the choice of a model of
the generic fibre, and that equidistribution of curves holds for smooth projective
split toric varieties. As an application, we study the Batyrev-Manin-Peyre principle
for curves on a certain kind of twisted products."
acknowledgement: I am very grateful to my Ph.D. advisor Emmanuel Peyre for all the
remarks and suggestions he made during the writing of this article. I warmly thank
Margaret Bilu and Tim Browning for some valuable comments they made on a preliminary
version of this work. I would like to thank David Bourqui as well for several helpful
conversations. Finally, I thank the anonymous referee for their very careful reading
and their numerous comments and suggestions which helped me a lot in improving the
exposition, besides fixing several typos, and Elizabeth Weaver for the final editing
work. During the revision process of this work, the author received funding from
the European Union’s Horizon 2020 research and innovation programme under the Marie
Skłodowska-Curie Grant Agreement No. 101034413.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Loïs
full_name: Faisant, Loïs
id: 26ca6926-5797-11ee-9232-f8b51bd19631
last_name: Faisant
citation:
ama: Faisant L. Motivic distribution of rational curves and twisted products of
toric varieties. Algebra & Number Theory. 2025;19:883-965. doi:10.2140/ant.2025.19.883
apa: Faisant, L. (2025). Motivic distribution of rational curves and twisted products
of toric varieties. Algebra & Number Theory. Mathematical Sciences
Publishers. https://doi.org/10.2140/ant.2025.19.883
chicago: Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products
of Toric Varieties.” Algebra & Number Theory. Mathematical Sciences
Publishers, 2025. https://doi.org/10.2140/ant.2025.19.883.
ieee: L. Faisant, “Motivic distribution of rational curves and twisted products
of toric varieties,” Algebra & Number Theory, vol. 19. Mathematical
Sciences Publishers, pp. 883–965, 2025.
ista: Faisant L. 2025. Motivic distribution of rational curves and twisted products
of toric varieties. Algebra & Number Theory. 19, 883–965.
mla: Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products
of Toric Varieties.” Algebra & Number Theory, vol. 19, Mathematical
Sciences Publishers, 2025, pp. 883–965, doi:10.2140/ant.2025.19.883.
short: L. Faisant, Algebra & Number Theory 19 (2025) 883–965.
corr_author: '1'
date_created: 2025-02-18T13:33:14Z
date_published: 2025-04-22T00:00:00Z
date_updated: 2026-02-17T13:19:19Z
day: '22'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.2140/ant.2025.19.883
ec_funded: 1
external_id:
arxiv:
- '2302.07339'
file:
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checksum: 56299f55682528a7cd0136497ce8b383
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file_name: 2025_AlgebraNumberTheory_Faisant.pdf
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language:
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oa: 1
oa_version: Published Version
page: 883-965
project:
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call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Algebra & Number Theory
publication_identifier:
eissn:
- 1944-7833
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
status: public
title: Motivic distribution of rational curves and twisted products of toric varieties
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: 19
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '19055'
abstract:
- lang: eng
text: "Using the formalism of Cox rings and universal torsors, we prove a decomposition
of the Grothendieck motive of the moduli space of morphisms from an arbitrary
smooth projective curve to a Mori Dream Space (MDS).\r\n For the simplest cases
of MDS, that of toric varieties, we use this decomposition to prove an instance
of the motivic Batyrev--Manin--Peyre principle for curves satisfying tangency
conditions with respect to the boundary divisors, often called Campana curves."
acknowledgement: "The author acknowledges funding from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement
No 101034413.\r\n"
article_number: '2502.11704'
article_processing_charge: No
arxiv: 1
author:
- first_name: Loïs
full_name: Faisant, Loïs
id: 26ca6926-5797-11ee-9232-f8b51bd19631
last_name: Faisant
citation:
ama: Faisant L. Motivic counting of rational curves with tangency conditions via
universal torsors. arXiv. doi:10.48550/ARXIV.2502.11704
apa: Faisant, L. (n.d.). Motivic counting of rational curves with tangency conditions
via universal torsors. arXiv. https://doi.org/10.48550/ARXIV.2502.11704
chicago: Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions
via Universal Torsors.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2502.11704.
ieee: L. Faisant, “Motivic counting of rational curves with tangency conditions
via universal torsors,” arXiv. .
ista: Faisant L. Motivic counting of rational curves with tangency conditions via
universal torsors. arXiv, 2502.11704.
mla: Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions
via Universal Torsors.” ArXiv, 2502.11704, doi:10.48550/ARXIV.2502.11704.
short: L. Faisant, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-02-18T13:34:07Z
date_published: 2025-02-17T00:00:00Z
date_updated: 2025-04-14T07:54:52Z
day: '17'
department:
- _id: TiBr
doi: 10.48550/ARXIV.2502.11704
ec_funded: 1
external_id:
arxiv:
- '2502.11704'
language:
- iso: eng
main_file_link:
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month: '02'
oa: 1
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project:
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call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: arXiv
publication_status: submitted
status: public
title: Motivic counting of rational curves with tangency conditions via universal
torsors
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '19363'
abstract:
- lang: eng
text: For a general family of non-negative functions matching upper and lower bounds
are established for their average over the values of any equidistributed sequence.
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Yik Tung
full_name: Chan, Yik Tung
id: c4c0afc8-9262-11ed-9231-d8b0bc743af1
last_name: Chan
orcid: 0000-0001-8467-4106
- first_name: Peter
full_name: Koymans, Peter
last_name: Koymans
- first_name: Carlo
full_name: Pagano, Carlo
last_name: Pagano
- first_name: Efthymios
full_name: Sofos, Efthymios
last_name: Sofos
citation:
ama: Chan S, Koymans P, Pagano C, Sofos E. Averages of multiplicative functions
along equidistributed sequences. Journal of Number Theory. 2025;273:1-36.
doi:10.1016/j.jnt.2025.01.005
apa: Chan, S., Koymans, P., Pagano, C., & Sofos, E. (2025). Averages of multiplicative
functions along equidistributed sequences. Journal of Number Theory. Elsevier.
https://doi.org/10.1016/j.jnt.2025.01.005
chicago: Chan, Stephanie, Peter Koymans, Carlo Pagano, and Efthymios Sofos. “Averages
of Multiplicative Functions along Equidistributed Sequences.” Journal of Number
Theory. Elsevier, 2025. https://doi.org/10.1016/j.jnt.2025.01.005.
ieee: S. Chan, P. Koymans, C. Pagano, and E. Sofos, “Averages of multiplicative
functions along equidistributed sequences,” Journal of Number Theory, vol.
273. Elsevier, pp. 1–36, 2025.
ista: Chan S, Koymans P, Pagano C, Sofos E. 2025. Averages of multiplicative functions
along equidistributed sequences. Journal of Number Theory. 273, 1–36.
mla: Chan, Stephanie, et al. “Averages of Multiplicative Functions along Equidistributed
Sequences.” Journal of Number Theory, vol. 273, Elsevier, 2025, pp. 1–36,
doi:10.1016/j.jnt.2025.01.005.
short: S. Chan, P. Koymans, C. Pagano, E. Sofos, Journal of Number Theory 273 (2025)
1–36.
corr_author: '1'
date_created: 2025-03-09T23:01:26Z
date_published: 2025-08-01T00:00:00Z
date_updated: 2025-12-30T08:06:16Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1016/j.jnt.2025.01.005
external_id:
isi:
- '001444208500001'
file:
- access_level: open_access
checksum: 752c407eb186d391380b10a7505f66cf
content_type: application/pdf
creator: dernst
date_created: 2025-12-30T08:05:42Z
date_updated: 2025-12-30T08:05:42Z
file_id: '20889'
file_name: 2025_JourNumberTheory_Chan.pdf
file_size: 685204
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file_date_updated: 2025-12-30T08:05:42Z
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isi: 1
language:
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month: '08'
oa: 1
oa_version: Published Version
page: 1-36
publication: Journal of Number Theory
publication_identifier:
issn:
- 0022-314X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Averages of multiplicative functions along equidistributed sequences
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: 273
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19407'
abstract:
- lang: eng
text: We discuss, in a non-Archimedean setting, the distribution of the coefficients
of L-polynomials of curves of genus g over Fq . Among other results, this allows
us to prove that the Q-vector space spanned by such characteristic polynomials
has dimension g + 1. We also state a conjecture about the Archimedean distribution
of the number of rational points of curves over finite fields.
acknowledgement: We thank Umberto Zannier for bringing the problem to our attention,
for many useful suggestions, and especially for pointing out the relevance of the
equidistribution results of Katz–Sarnak, noting that they imply the case q≫g0 of
theorem 1.4. In addition, the first author would like to thank Umberto Zannier for
his guidance during his undergraduate studies, on a topic that ultimately inspired
much of the work in this article. We are grateful to J. Kaczorowski and A. Perelli
for sharing their work [Reference Kaczorowski and Perelli28] before publication.
We thank Christophe Ritzenthaler and Elisa Lorenzo García for their interesting
comments on the first version of this article, Zhao Yu Ma for a comment about remark
3.12, and the anonymous referees for their helpful suggestions.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Francesco
full_name: Ballini, Francesco
last_name: Ballini
- first_name: Davide
full_name: Lombardo, Davide
last_name: Lombardo
- first_name: Matteo
full_name: Verzobio, Matteo
id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
last_name: Verzobio
orcid: 0000-0002-0854-0306
citation:
ama: 'Ballini F, Lombardo D, Verzobio M. On the L-polynomials of curves over finite
fields. Proceedings of the Royal Society of Edinburgh Section A: Mathematics.
2025. doi:10.1017/prm.2025.7'
apa: 'Ballini, F., Lombardo, D., & Verzobio, M. (2025). On the L-polynomials
of curves over finite fields. Proceedings of the Royal Society of Edinburgh
Section A: Mathematics. Cambridge University Press. https://doi.org/10.1017/prm.2025.7'
chicago: 'Ballini, Francesco, Davide Lombardo, and Matteo Verzobio. “On the L-Polynomials
of Curves over Finite Fields.” Proceedings of the Royal Society of Edinburgh
Section A: Mathematics. Cambridge University Press, 2025. https://doi.org/10.1017/prm.2025.7.'
ieee: 'F. Ballini, D. Lombardo, and M. Verzobio, “On the L-polynomials of curves
over finite fields,” Proceedings of the Royal Society of Edinburgh Section
A: Mathematics. Cambridge University Press, 2025.'
ista: 'Ballini F, Lombardo D, Verzobio M. 2025. On the L-polynomials of curves over
finite fields. Proceedings of the Royal Society of Edinburgh Section A: Mathematics.'
mla: 'Ballini, Francesco, et al. “On the L-Polynomials of Curves over Finite Fields.”
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Cambridge
University Press, 2025, doi:10.1017/prm.2025.7.'
short: 'F. Ballini, D. Lombardo, M. Verzobio, Proceedings of the Royal Society of
Edinburgh Section A: Mathematics (2025).'
corr_author: '1'
date_created: 2025-03-16T23:01:25Z
date_published: 2025-02-06T00:00:00Z
date_updated: 2025-09-30T11:00:35Z
day: '06'
department:
- _id: TiBr
doi: 10.1017/prm.2025.7
external_id:
isi:
- '001414690400001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1017/prm.2025.7
month: '02'
oa: 1
oa_version: Published Version
publication: 'Proceedings of the Royal Society of Edinburgh Section A: Mathematics'
publication_identifier:
eissn:
- 1473-7124
issn:
- 0308-2105
publication_status: epub_ahead
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the L-polynomials of curves over finite fields
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '19483'
abstract:
- lang: eng
text: We prove matching upper and lower bounds for the average of the6-torsionof
class groups of quadratic fields. Furthermore, we count the number of integer
solutions on an affine quartic threefold.
article_number: '18'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yik Tung
full_name: Chan, Yik Tung
id: c4c0afc8-9262-11ed-9231-d8b0bc743af1
last_name: Chan
orcid: 0000-0001-8467-4106
- first_name: Peter
full_name: Koymans, Peter
last_name: Koymans
- first_name: Carlo
full_name: Pagano, Carlo
last_name: Pagano
- first_name: Efthymios
full_name: Sofos, Efthymios
last_name: Sofos
citation:
ama: Chan S, Koymans P, Pagano C, Sofos E. 6-torision and integral points on quartic
threefolds. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
2025. doi:10.2422/2036-2145.202412_006
apa: Chan, S., Koymans, P., Pagano, C., & Sofos, E. (2025). 6-torision and integral
points on quartic threefolds. Annali Della Scuola Normale Superiore Di Pisa,
Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale. https://doi.org/10.2422/2036-2145.202412_006
chicago: Chan, Stephanie, Peter Koymans, Carlo Pagano, and Efthymios Sofos. “6-Torision
and Integral Points on Quartic Threefolds.” Annali Della Scuola Normale Superiore
Di Pisa, Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale,
2025. https://doi.org/10.2422/2036-2145.202412_006.
ieee: S. Chan, P. Koymans, C. Pagano, and E. Sofos, “6-torision and integral points
on quartic threefolds,” Annali della Scuola Normale Superiore di Pisa, Classe
di Scienze. Scuola Normale Superiore - Edizioni della Normale, 2025.
ista: Chan S, Koymans P, Pagano C, Sofos E. 2025. 6-torision and integral points
on quartic threefolds. Annali della Scuola Normale Superiore di Pisa, Classe di
Scienze., 18.
mla: Chan, Stephanie, et al. “6-Torision and Integral Points on Quartic Threefolds.”
Annali Della Scuola Normale Superiore Di Pisa, Classe Di Scienze, 18, Scuola
Normale Superiore - Edizioni della Normale, 2025, doi:10.2422/2036-2145.202412_006.
short: S. Chan, P. Koymans, C. Pagano, E. Sofos, Annali Della Scuola Normale Superiore
Di Pisa, Classe Di Scienze (2025).
corr_author: '1'
date_created: 2025-04-05T10:49:27Z
date_published: 2025-03-07T00:00:00Z
date_updated: 2025-05-14T11:40:24Z
day: '07'
department:
- _id: TiBr
doi: 10.2422/2036-2145.202412_006
external_id:
arxiv:
- '2403.13359'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2403.13359'
month: '03'
oa: 1
oa_version: Preprint
publication: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
publication_identifier:
eissn:
- 2036-2145
issn:
- 0391-173X
publication_status: epub_ahead
publisher: Scuola Normale Superiore - Edizioni della Normale
status: public
title: 6-torision and integral points on quartic threefolds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: publisher
OA_type: diamond
_id: '19673'
abstract:
- lang: eng
text: We show that almost all primes p =\= ± 4 mod9 are sums of three cubes, assuming
a conjecture due to Hooley, Manin, et al. on cubic fourfolds. This conjecture
is approachable under standard statistical hypotheses on geometric families of
L-functions.
acknowledgement: This work was partially supported by the European Union’s Horizon
2020 research and innovation program under the MarieSkłodowska-Curie Grant Agreement
No. 101034413
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Victor
full_name: Wang, Victor
id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
last_name: Wang
orcid: 0000-0002-0704-7026
citation:
ama: Wang V. Prime Hasse principles via diophantine second moments. Journal of
the Association for Mathematical Research. 2025;3(1):1-26. doi:10.56994/JAMR.003.001.001
apa: Wang, V. (2025). Prime Hasse principles via diophantine second moments. Journal
of the Association for Mathematical Research. Association for Mathematical
Research. https://doi.org/10.56994/JAMR.003.001.001
chicago: Wang, Victor. “Prime Hasse Principles via Diophantine Second Moments.”
Journal of the Association for Mathematical Research. Association for Mathematical
Research, 2025. https://doi.org/10.56994/JAMR.003.001.001.
ieee: V. Wang, “Prime Hasse principles via diophantine second moments,” Journal
of the Association for Mathematical Research, vol. 3, no. 1. Association for
Mathematical Research, pp. 1–26, 2025.
ista: Wang V. 2025. Prime Hasse principles via diophantine second moments. Journal
of the Association for Mathematical Research. 3(1), 1–26.
mla: Wang, Victor. “Prime Hasse Principles via Diophantine Second Moments.” Journal
of the Association for Mathematical Research, vol. 3, no. 1, Association for
Mathematical Research, 2025, pp. 1–26, doi:10.56994/JAMR.003.001.001.
short: V. Wang, Journal of the Association for Mathematical Research 3 (2025) 1–26.
corr_author: '1'
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abstract:
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text: By studying some Clausen-like multiple Dirichlet series, we complete the proof
of Manin's conjecture for sufficiently split smooth equivariant compactifications
of the translation-dilation group over the rationals. Secondary terms remain elusive
in general.
acknowledgement: I thank Yuri Tschinkel for introducing me to the beautiful paper
[53] and associated open questions, and thank him as well as Ramin Takloo-Bighash
and Sho Tanimoto for their encouragement and comments. Also, I thank Tim Browning
and Dan Loughran for comments and suggestions concerning Manin–Peyre, homogeneous
spaces, and splitness. Thanks also to Anshul Adve, Peter Sarnak, Philip Tosteson,
Katy Woo, and Nina Zubrilina for some interesting discussions. I thank the Browning
Group and Andy O'Desky for many conversations. This project has received funding
from the European Union's Horizon 2020 research and innovation program under the
Marie Skłodowska-Curie Grant Agreement No. 101034413. Finally, I thank the editors
and referees for their detailed input, which substantially improved the paper.
article_number: '110341'
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author:
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full_name: Wang, Victor
id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9
last_name: Wang
orcid: 0000-0002-0704-7026
citation:
ama: Wang V. Asymptotic growth of translation-dilation orbits. Advances in Mathematics.
2025;475. doi:10.1016/j.aim.2025.110341
apa: Wang, V. (2025). Asymptotic growth of translation-dilation orbits. Advances
in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2025.110341
chicago: Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” Advances
in Mathematics. Elsevier, 2025. https://doi.org/10.1016/j.aim.2025.110341.
ieee: V. Wang, “Asymptotic growth of translation-dilation orbits,” Advances in
Mathematics, vol. 475. Elsevier, 2025.
ista: Wang V. 2025. Asymptotic growth of translation-dilation orbits. Advances in
Mathematics. 475, 110341.
mla: Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” Advances
in Mathematics, vol. 475, 110341, Elsevier, 2025, doi:10.1016/j.aim.2025.110341.
short: V. Wang, Advances in Mathematics 475 (2025).
corr_author: '1'
date_created: 2025-05-25T22:16:41Z
date_published: 2025-07-01T00:00:00Z
date_updated: 2025-12-30T08:30:30Z
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doi: 10.1016/j.aim.2025.110341
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title: Asymptotic growth of translation-dilation orbits
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abstract:
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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'
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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
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name: Rational curves via function field analytic number theory
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