Roth's theorem in the primes

BJ Green

Research output: Contribution to journalArticle (Academic Journal)peer-review

94 Citations (Scopus)


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.
Translated title of the contributionRoth's theorem in the primes
Original languageEnglish
Pages (from-to)1609 - 1636
JournalAnnals of Mathematics
Volume161 (3)
Publication statusPublished - May 2005

Bibliographical note

Publisher: Ann Mathematics
Other identifier: IDS Number: 980YR


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