Variations on the Sum-Product Problem

Brendan Murphy, Oliver Roche-Newton, Ilya D. Shkredov

This paper considers various formulations of the sum-product problem. It is shown that, for a finite set $A\subset \mathbb{R}$, $$|A(A+A)|\gg |A{|}^{\frac{3}{2}+\frac{1}{178}},$$ g…