Roth's theorem in the primes
Number Theory
2007-05-23 v3 Classical Analysis and ODEs
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.
Cite
@article{arxiv.math/0302311,
title = {Roth's theorem in the primes},
author = {Ben Green},
journal= {arXiv preprint arXiv:math/0302311},
year = {2007}
}
Comments
23 pages. Updated references and made some minor changes recommended by the referee. To appear in Annals of Mathematics