On the size of the set AA+A

It is established that there exists an absolute constant c>0 such that for any finite set A of positive real numbers |AA+A|≫|A|32+c.On the other hand, we give an explicit construction of a finite set A⊂R such that |AA+A|=o(|A|2), disproving a conjecture of Balog.

Saved in:
Bibliographic Details
Published in:Journal of the London Mathematical Society 2019-04, Vol.99 (2), p.477-494
Main Authors: Roche‐Newton, Oliver, Ruzsa, Imre Z., Shen, Chun‐Yen, Shkredov, Ilya D.
Format: Article
Language:English
Subjects:
11B30 (secondary)
52C10 (primary)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is established that there exists an absolute constant c>0 such that for any finite set A of positive real numbers |AA+A|≫|A|32+c.On the other hand, we give an explicit construction of a finite set A⊂R such that |AA+A|=o(|A|2), disproving a conjecture of Balog.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms.12177