Roth's theorem in the primes

• Autores: Benjamin Green
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 161, Nº 3, 2005, págs. 1609-1636
• Idioma: inglés
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• Resumen

  • 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.