Key points are not available for this paper at this time.
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.
Ben Green (Sun,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: