A proof of a sumset conjecture of Erdos

Joel Moreira, Florian K. Richter, Donald Robertson

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

In this paper we show that every set A⊂ℕ with positive density contains B+C for some pair B,C of infinite subsets of ℕ, settling a conjecture of Erdos. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups.

Original languageEnglish (US)
Pages (from-to)605-652
Number of pages48
JournalAnnals of Mathematics
Volume189
Issue number2
DOIs
StatePublished - Mar 1 2019

Keywords

  • Almost periodic functions
  • Sum sets
  • Ultrafilters

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'A proof of a sumset conjecture of Erdos'. Together they form a unique fingerprint.

Cite this