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Title: A proof of a sumset conjecture of Erdős
Award ID(s):
1703597
NSF-PAR ID:
10315759
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Annals of Mathematics
Volume:
189
Issue:
2
ISSN:
0003-486X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. 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 Erd\H os. 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. 
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