On a question of A. Balog

Ilya D. Shkredov

Vol. 280 (2016), No. 1, 227–240

DOI: 10.2140/pjm.2016.280.227

Abstract

We give a partial answer to a conjecture of A. Balog concerning the size of $AA+A$, where $A$ is a finite subset of real numbers. We also prove several new results on the cardinality of $A:A+A$, $AA+AA$ and $A:A+A:A$.

Keywords

sum-products, Szemerédi–Trotter theorem

Mathematical Subject Classification 2010

Primary: 11B13, 11B75

Milestones

Received: 2 February 2015

Revised: 23 May 2015

Accepted: 26 May 2015

Published: 28 December 2015