Roth's theorem in the primes

@article{Green2003RothsTI,
  title={Roth's theorem in the primes},
  author={B. Green},
  journal={Annals of Mathematics},
  year={2003},
  volume={161},
  pages={1609-1636}
}
  • B. Green
  • Published 2003
  • Mathematics
  • Annals of Mathematics
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. 

Paper Mentions

Szemerédi's Theorem in the Primes
A Density Version of the Vinogradov Three Primes Theorem
A New Proof of Vinogradov's Three Primes Theorem
Arithmetic structures in random sets
Partition regularity and the primes
A multidimensional Szemerédi's theorem in the primes
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