If $A+A$ is small then $AAA$ is superquadratic

Abstract

This note proves that there exists positive constants $c_1$ and $c_2$ such that for all finite $A\subset \mathbb{R}$ with $|A+A|\le |A{|}^{1+c_1}$ we have $|AAA|\gg |A{|}^{2+c_2}$.

This updated version contains some extra results using the same methods. The main change is the addition of Theorem 1.3, which proves a superquadratic bound for the triple product of a sum set

References in corpus (1)

• New Proofs of Plünnecke-type Estimates for Product Sets in Groups