English

Generalising the Hardy-Littlewood Method for Primes

Number Theory 2007-05-23 v1

Abstract

The Hardy-Littlewood method is a well-known technique in analytic number theory. Among its spectacular applications are Vinogradov's 1937 result that every sufficiently large odd number is a sum of three primes, and a related result of Chowla and Van der Corput giving an asymptotic for the number of 3-term progressions of primes, all less than N. This article surveys recent developments of the author and T. Tao, in which the Hardy-Littlewood method has been generalised to obtain, for example, an asymptotic for the number of 4-term arithmetic progressions of primes less than N.

Keywords

Cite

@article{arxiv.math/0601211,
  title  = {Generalising the Hardy-Littlewood Method for Primes},
  author = {Ben Green},
  journal= {arXiv preprint arXiv:math/0601211},
  year   = {2007}
}

Comments

26 pages, submitted to Proceedings of ICM 2006

R2 v1 2026-07-22T17:29:45.721Z