Geodesic
Roth’s theorem in the primes
Ben Green1
1 Department of Pure Mathematics and Mathematical Statistics, Trinity College, University of Cambridge, Cambridge CB3 0WB, United Kingdom
Annals of mathematics, Tome 161 (2005) no. 3, pp. 1609-1636.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2005.161.1609

Ben Green 1

1 Department of Pure Mathematics and Mathematical Statistics, Trinity College, University of Cambridge, Cambridge CB3 0WB, United Kingdom 
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Ben Green. Roth’s theorem in the primes. Annals of mathematics, Tome 161 (2005) no. 3, pp. 1609-1636. doi : 10.4007/annals.2005.161.1609. http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.161.1609/

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