---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '22618'
abstract:
- lang: eng
  text: "We use a function field version of the circle method to prove that a positive
    proportion of elements in \U0001D53D\U0001D45E⁡[\U0001D461] are representable
    as a sum of three cubes of minimal degree from \U0001D53D\U0001D45E⁡[\U0001D461],
    assuming a suitable form of the Ratios Conjecture and that char⁡(\U0001D53D\U0001D45E)
    >3. The analogue of this conjecture for quadratic Dirichlet L-functions is known
    for large fixed q, via recent developments in homological stability."
acknowledgement: While working on this paper the first two authors were supported
  by 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, and by the National Science and Technology Council
  Project Grant 114-2115-M-001-010-MY2.
article_number: e112
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: 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. Sums of three cubes over a function field. <i>Forum
    of Mathematics Sigma</i>. 2026;14. doi:<a href="https://doi.org/10.1017/fms.2026.10259">10.1017/fms.2026.10259</a>
  apa: Browning, T. D., Glas, J., &#38; Wang, V. (2026). Sums of three cubes over
    a function field. <i>Forum of Mathematics Sigma</i>. Cambridge University Press.
    <a href="https://doi.org/10.1017/fms.2026.10259">https://doi.org/10.1017/fms.2026.10259</a>
  chicago: Browning, Timothy D, Jakob Glas, and Victor Wang. “Sums of Three Cubes
    over a Function Field.” <i>Forum of Mathematics Sigma</i>. Cambridge University
    Press, 2026. <a href="https://doi.org/10.1017/fms.2026.10259">https://doi.org/10.1017/fms.2026.10259</a>.
  ieee: T. D. Browning, J. Glas, and V. Wang, “Sums of three cubes over a function
    field,” <i>Forum of Mathematics Sigma</i>, vol. 14. Cambridge University Press,
    2026.
  ista: Browning TD, Glas J, Wang V. 2026. Sums of three cubes over a function field.
    Forum of Mathematics Sigma. 14, e112.
  mla: Browning, Timothy D., et al. “Sums of Three Cubes over a Function Field.” <i>Forum
    of Mathematics Sigma</i>, vol. 14, e112, Cambridge University Press, 2026, doi:<a
    href="https://doi.org/10.1017/fms.2026.10259">10.1017/fms.2026.10259</a>.
  short: T.D. Browning, J. Glas, V. Wang, Forum of Mathematics Sigma 14 (2026).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-08-02T22:01:52Z
date_published: 2026-07-22T00:00:00Z
date_updated: 2026-08-03T12:13:59Z
day: '22'
ddc:
- '500'
department:
- _id: TiBr
- _id: GradSch
doi: 10.1017/fms.2026.10259
ec_funded: 1
external_id:
  arxiv:
  - '2402.07146'
file:
- access_level: open_access
  checksum: e92a762e03f832bdca8c106a9a88ef9b
  content_type: application/pdf
  creator: dernst
  date_created: 2026-08-03T12:12:03Z
  date_updated: 2026-08-03T12:12:03Z
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  file_size: 810718
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file_date_updated: 2026-08-03T12:12:03Z
fulldoi: https://doi.org/10.1017/fms.2026.10259
has_accepted_license: '1'
intvolume: '        14'
language:
- iso: eng
month: '07'
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: Forum of Mathematics Sigma
publication_identifier:
  eissn:
  - 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Sums of three cubes over a function field
tmp:
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  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: 14
year: '2026'
...