Optimal sums of three cubes in Fq[t]
Browning TD, Glas J, Wang V. 2025. Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. 310(4), 65.
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Abstract
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.
Publishing Year
Date Published
2025-05-23
Journal Title
Mathematische Zeitschrift
Publisher
Springer Nature
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).
Volume
310
Issue
4
Article Number
65
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IST-REx-ID
Cite this
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
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
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.
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.
Browning TD, Glas J, Wang V. 2025. Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. 310(4), 65.
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.
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