Roth's theorem in the primes

Details Roth's theorem in the primes Roth's theorem in the primes

2003-02-25

arxiv.org/abs/math/0302311v3

Mathematics

Number Theory

23 pages. Updated references and made some minor changes recommended by the referee. To appear in Annals of Mathematics

Scientific paper

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.

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