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arXiv · 2408.03668

Optimal sums of three cubes in $\mathbb{F}_q[t]$

Tim Browning·Jakob Glas·Victor Y. Wang
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Abstract

We use the circle method to prove that a density 1 of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of essentially minimal degree from $\mathbb{F}_q[t]$, assuming the Ratios Conjecture and that the characteristic is bigger than 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.

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Tim Browning, Jakob Glas, Victor Y. Wang. 2024-08-07. Optimal sums of three cubes in $\mathbb{F}_q[t]$. https://doi.org/10.1007/s00209-025-03765-z

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