Roth's theorem in the primes

• 成果类型: Article
• 署名作者: Green, B
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.161.1609
• 发表日期: 2005
• 页码: 1609-1636
• 关键词: no arithmetic progressions; integer sets; RESTRICTION

摘要

We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes.