On the size of the set AA+A

Oliver Roche-Newton, Imre Z. Ruzsa, Chun Yen Shen, Ilya D. Shkredov

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Abstract

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| 3/2+c On the other hand, we give an explicit construction of a finite set (Formula presented.) such that |AA + A| = o(|A|2), disproving a conjecture of Balog.

Original languageEnglish
Pages (from-to)477-494
Number of pages18
JournalJournal of the London Mathematical Society
Volume99
Issue number2
DOIs
Publication statusPublished - Apr 2019

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ASJC Scopus subject areas

  • Mathematics(all)

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