On almost Cap sets in three variables and the multivariable Cap set problem

Abstract

In this note we prove that almost cap sets $A\subset {\mathbb{F}}_q^n$, i.e., the subsets of ${\mathbb{F}}_q^n$ that do not contain too many arithmetic progressions of length three, satisfy that $|A|<c_q^n$ for some $c_q<q$. As a corollary we prove a multivariable analogue of Ellenberg-Gijswijt theorem.

5 pages

References in corpus (1)

• Progression-free sets in Z_4^n are exponentially small