Roth's theorem in the primes

@article{Green2003RothsTI,
  title={Roth's theorem in the primes},
  author={Ben Green},
  journal={Annals of Mathematics},
  year={2003},
  volume={161},
  pages={1609-1636}
}
  • B. Green
  • Published 25 February 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. 
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163 Citations
Highly Influential Citations
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Methods Citations
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Results Citations
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163 Citations

Ju l 2 00 3 Roth ’ s Theorem in the Primes

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…

2 5 Fe b 20 03 Roth ’ s Theorem in the Primes

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