Sums of three cubes over a function field
Browning TD, Glas J, Wang V. 2026. Sums of three cubes over a function field. Forum of Mathematics Sigma. 14, e112.
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Abstract
We use a function field version of the circle method to prove that a positive proportion of elements in π½πβ‘[π‘] are representable as a sum of three cubes of minimal degree from π½πβ‘[π‘], assuming a suitable form of the Ratios Conjecture and that charβ‘(π½π) >3. The analogue of this conjecture for quadratic Dirichlet L-functions is known for large fixed q, via recent developments in homological stability.
Publishing Year
Date Published
2026-07-22
Journal Title
Forum of Mathematics Sigma
Publisher
Cambridge University Press
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 Unionβs Horizon 2020 research and innovation programme under the Marie SkΕodowska-Curie Grant Agreement No. 101034413, and by the National Science and Technology Council Project Grant 114-2115-M-001-010-MY2.
Volume
14
Article Number
e112
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IST-REx-ID
Cite this
Browning TD, Glas J, Wang V. Sums of three cubes over a function field. Forum of Mathematics Sigma. 2026;14. doi:10.1017/fms.2026.10259
Browning, T. D., Glas, J., & Wang, V. (2026). Sums of three cubes over a function field. Forum of Mathematics Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2026.10259
Browning, Timothy D, Jakob Glas, and Victor Wang. βSums of Three Cubes over a Function Field.β Forum of Mathematics Sigma. Cambridge University Press, 2026. https://doi.org/10.1017/fms.2026.10259.
T. D. Browning, J. Glas, and V. Wang, βSums of three cubes over a function field,β Forum of Mathematics Sigma, vol. 14. Cambridge University Press, 2026.
Browning TD, Glas J, Wang V. 2026. Sums of three cubes over a function field. Forum of Mathematics Sigma. 14, e112.
Browning, Timothy D., et al. βSums of Three Cubes over a Function Field.β Forum of Mathematics Sigma, vol. 14, e112, Cambridge University Press, 2026, doi:10.1017/fms.2026.10259.
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