Abstract
We show that if f(u) ∈ Z[u] is a monic cubic polynomial, then for all but finitely many n∈ Z the affine cubic surface f(u1)+f(u2)+f(u3)=n⊂AZ3 has no integral Brauer-Manin obstruction to the Hasse principle.
| Original language | English |
|---|---|
| Pages (from-to) | 1305-1331 |
| Number of pages | 27 |
| Journal | Manuscripta Mathematica |
| Volume | 173 |
| Issue number | 3-4 |
| Early online date | 2 Aug 2023 |
| DOIs | |
| Publication status | Published - 31 Mar 2024 |
Funding
The author would like thank Daniel Loughran for his insights and tireless support and Jörg Jahnel for donating his Magma code for computing the Brauer group of smooth cubic surfaces. They would also like to thank Sam Streeter and Olivier Wittenberg for comments on early revisions of this paper, J.-L. Colliot-Thélène for pointing out the sum of three cubes conjecture was first presented as a question of Mordell in the literature and the anonymous referee for many valuable comments and corrections.
Keywords
- 11D25
- 14F22 (Secondary)
- 14G05
- 14G12 (Primary)
ASJC Scopus subject areas
- General Mathematics