Uniform sets with few progressions via colorings

Mingyang Deng, Jonathan Tidor, Yufei Zhao

Ruzsa asked whether there exist Fourier-uniform subsets of $\mathbb{Z}/N\mathbb{Z}$ with density $\hat{I}\pm$ and 4-term arithmetic progression (4-AP) density at most $\hat{I}{\pm }^C$, for arbitrarily…