On the size of the set AA+A

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

Research output: Contribution to journalArticle

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 A ⊂ R such that |AA + A| = o(|A|2), disproving a conjecture of Balog.

Original languageEnglish
JournalJournal of the London Mathematical Society
DOIs
Publication statusAccepted/In press - Jan 1 2018

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Finite Set

Keywords

  • 11B30 (secondary)
  • 52C10 (primary)

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the size of the set AA+A. / Roche-Newton, Oliver; Ruzsa, I.; Shen, Chun Yen; Shkredov, Ilya D.

In: Journal of the London Mathematical Society, 01.01.2018.

Research output: Contribution to journalArticle

Roche-Newton, Oliver ; Ruzsa, I. ; Shen, Chun Yen ; Shkredov, Ilya D. / On the size of the set AA+A. In: Journal of the London Mathematical Society. 2018.
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