Low-complexity approximations for sets defined by generalizations of affine conditions

W. T. Gowers, Thomas Karam

Let $p$ be a prime, let $S$ be a non-empty subset of ${\mathbb{F}}_p$ and let $0<\epsilon \le 1$. We show that there exists a constant $C=C(p,\epsilon )$ such that for every positive integer $k$,…