Oliver Roche-Newton, Ilya D. Shkredov·2018-10-25·via math.CO updates on arXiv.org
This note proves that there exists positive constants $c_1$ and $c_2$ such that for all finite $A \subset \mathbb R$ with $|A+A| \leq |A|^{1+c_1}$ we have $|AAA| \gg |A|^{2+c_2}$.