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

authored by

Tim Browning, Jakob Glas, Victor Y. Wang

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Institute of Science and Technology Austria (ISTA)

Type

Article

Journal

Mathematische Zeitschrift

Volume

310

ISSN

0025-5874

Publication date

23.05.2025

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics

Electronic version(s)

https://doi.org/10.1007/s00209-025-03765-z (Access: Open)