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

verfasst von

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Institute of Science and Technology Austria

Typ

Artikel

Journal

Mathematische Zeitschrift

Band

310

ISSN

0025-5874

Publikationsdatum

23.05.2025

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Allgemeine Mathematik

Elektronische Version(en)

https://doi.org/10.1007/s00209-025-03765-z (Zugang: Offen)