Ben Green's Open Problem 57
Prior state unknown→disproved
intended complex form disproved, with a certified strict support-function gap
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analysis / Higher-order Fourier analysis
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.
15Significance / 100
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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.
intended complex form disproved, with a certified strict support-function gap
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