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

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.

23 pages

References in corpus (1)

• Conjectures for the integral moments and ratios of L-functions over function fields