[{"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.","oa_version":"Published Version","external_id":{"arxiv":["2402.07146"]},"arxiv":1,"publisher":"Cambridge University Press","file_date_updated":"2026-08-03T12:12:03Z","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2026","has_accepted_license":"1","month":"07","intvolume":"        14","article_type":"original","das_tickbox":"0","file":[{"content_type":"application/pdf","access_level":"open_access","creator":"dernst","checksum":"e92a762e03f832bdca8c106a9a88ef9b","file_name":"2026_ForumMathematics_Browning.pdf","file_size":810718,"success":1,"relation":"main_file","date_created":"2026-08-03T12:12:03Z","file_id":"22636","date_updated":"2026-08-03T12:12:03Z"}],"abstract":[{"lang":"eng","text":"We use a function field version of the circle method to prove that a positive proportion of elements in 𝔽𝑞⁡[𝑡] are representable as a sum of three cubes of minimal degree from 𝔽𝑞⁡[𝑡], assuming a suitable form of the Ratios Conjecture and that char⁡(𝔽𝑞) >3. The analogue of this conjecture for quadratic Dirichlet L-functions is known for large fixed q, via recent developments in homological stability."}],"DOAJ_listed":"1","scopus_import":"1","article_number":"e112","date_updated":"2026-08-03T12:13:59Z","department":[{"_id":"TiBr"},{"_id":"GradSch"}],"_id":"22618","title":"Sums of three cubes over a function field","project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"},{"call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"OA_type":"gold","volume":14,"oa":1,"OA_place":"publisher","publication_status":"published","PlanS_conform":"1","publication":"Forum of Mathematics Sigma","ec_funded":1,"doi":"10.1017/fms.2026.10259","type":"journal_article","researchdata_availability":"no","supplementarymaterial":"no","language":[{"iso":"eng"}],"article_processing_charge":"Yes","citation":{"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>.","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>","short":"T.D. Browning, J. Glas, V. Wang, Forum of Mathematics Sigma 14 (2026).","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.","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>"},"status":"public","date_published":"2026-07-22T00:00:00Z","day":"22","corr_author":"1","date_created":"2026-08-02T22:01:52Z","author":[{"first_name":"Timothy D","full_name":"Browning, Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"},{"id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","last_name":"Glas","full_name":"Glas, Jakob","first_name":"Jakob"},{"first_name":"Victor","full_name":"Wang, Victor","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","orcid":"0000-0002-0704-7026","last_name":"Wang"}],"ddc":["500"],"publication_identifier":{"eissn":["2050-5094"]}}]