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

Oliver Roche-Newton; Ilya D. Shkredov

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

Combinatorics 2019-04-03 v2

Authors: Oliver Roche-Newton , Ilya D. Shkredov

Abstract

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

Cite

@article{arxiv.1810.10842,
  title  = {If $A+A$ is small then $AAA$ is superquadratic},
  author = {Oliver Roche-Newton and Ilya D. Shkredov},
  journal= {arXiv preprint arXiv:1810.10842},
  year   = {2019}
}

Comments

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

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

Abstract

Cite

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