A proof of a sumset conjecture of Erdos

• 成果类型: Article
• 署名作者: Moreira, Joel; Richter, Florian K.; Robertson, Donald
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2019.189.2.4
• 发表日期: 2019
• 页码: 605-652
• 关键词: sets; CONVERGENCE; SEQUENCES; averages

摘要

In this paper we show that every set A subset of 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.