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.
Translated title of the contribution | Roth's theorem in the primes |
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Original language | English |
Pages (from-to) | 1609 - 1636 |
Journal | Annals of Mathematics |
Volume | 161 (3) |
Publication status | Published - May 2005 |
Bibliographical note
Publisher: Ann MathematicsOther identifier: IDS Number: 980YR