Moderate-doubling sets in ${\mathbb{F}}_2^n$ intersect subspaces

Abstract

We show that any set $A$ in ${\mathbb{F}}_2^n$ with $|A+A|\le |A{|}^{2-\eta }$ must intersect a subspace of dimension $O_{\eta }(\log |A|)$ in at least $|A{|}^{\eta -o(1)}$ elements.

arXiv comment20 pages