Sums of three cubes over a function field

article Sums of three cubes over a function field published yes Timothy D Browning author 35827D50-F248-11E8-B48F-1D18A9856A870000-0002-8314-0177 Jakob Glas author d6423cba-dc74-11ea-a0a7-ee61689ff5fb Victor Wang author 76096395-aea4-11ed-a680-ab8ebbd3f1b90000-0002-0704-7026 TiBr department GradSch department Rational curves via function field analytic number theory project IST-BRIDGE: International postdoctoral program project 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. https://research-explorer.ista.ac.at/download/22618/22636/2026_ForumMathematics_Browning.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Cambridge University Press2026 eng Forum of Mathematics Sigma 2050-5094 2402.0714610.1017/fms.2026.10259 14 Browning, Timothy D, Jakob Glas, and Victor Wang. “Sums of Three Cubes over a Function Field.” Forum of Mathematics Sigma. Cambridge University Press, 2026. <a href="https://doi.org/10.1017/fms.2026.10259">https://doi.org/10.1017/fms.2026.10259</a>. T. D. Browning, J. Glas, and V. Wang, “Sums of three cubes over a function field,” Forum of Mathematics Sigma, vol. 14. Cambridge University Press, 2026. T.D. Browning, J. Glas, V. Wang, Forum of Mathematics Sigma 14 (2026). Browning, Timothy D., et al. “Sums of Three Cubes over a Function Field.” Forum of Mathematics Sigma, vol. 14, e112, Cambridge University Press, 2026, doi:<a href="https://doi.org/10.1017/fms.2026.10259">10.1017/fms.2026.10259</a>. Browning TD, Glas J, Wang V. Sums of three cubes over a function field. Forum of Mathematics Sigma. 2026;14. doi:<a href="https://doi.org/10.1017/fms.2026.10259">10.1017/fms.2026.10259</a> Browning TD, Glas J, Wang V. 2026. Sums of three cubes over a function field. Forum of Mathematics Sigma. 14, e112. Browning, T. D., Glas, J., & Wang, V. (2026). Sums of three cubes over a function field. Forum of Mathematics Sigma. Cambridge University Press. <a href="https://doi.org/10.1017/fms.2026.10259">https://doi.org/10.1017/fms.2026.10259</a> 226182026-08-02T22:01:52Z2026-08-03T12:13:59Z