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research article
A proof of a sumset conjecture of Erdős
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 Erdős. 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.
Type
research article
ArXiv ID
1803.00498
Authors
Publication date
2019
Published in
Volume
189
Issue
2
Start page
605
End page
652
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
November 26, 2021
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