A proof of a sumset conjecture of Erdős
- Award ID(s):
- 1703597
- NSF-PAR ID:
- 10315759
- 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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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.more » « less