## Roth’s Theorem in the primes

by
Ben Green

Venue: | Annals of Math |

Citations: | 21 - 4 self |

### BibTeX

@ARTICLE{Green_roth’stheorem,

author = {Ben Green},

title = {Roth’s Theorem in the primes},

journal = {Annals of Math},

year = {},

volume = {161},

pages = {1609--1636}

}

### OpenURL

### Abstract

Abstract. 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. 1.