Multi-fold sums from a set with few products

Abstract

In this paper we show that for any $k\ge 2$, there exist two universal constants $C_k,D_k>0$, such that for any finite subset $A$ of positive real numbers with $|AA|\le M|A|$, $|kA|\ge \frac{C_k}{M^{D_k}}\cdot |A{|}^{{\log }_{4}2k}.$

Cited by in corpus (1)

• On a theorem of Schoen and Shkredov on sumsets of convex sets