Ben Green's Open Problem 57

For a finite abelian group $G$, let $\Phi(G)$ be the absolutely convex hull of the specified trilinear kernels and $\Phi'(G)$ its restriction where the third factor depends only on $x_1 + x_2$. Is $\Phi(G) = \Phi'(G)$? A counterexample over $\mathbb{Z}/3\mathbb{Z}$ separates the hulls.

Result

Disproved(see note)

Status

Resolved

AI contribution

AI-discovered

Method

Construction

Field

Higher-order Fourier analysis

Posed by

Ben Green

Year posed

2024

Years open

2y

Solved

2026-05-21

Model

AlphaProof Nexus

Vendor

Google DeepMind

Collaborators

—

Verification

Lean-verified

Publication

Preprint

Significance

15 / 100*

Disclosed cost

—

Wikipedia

No dedicated article