## Generalising the Hardy-Littlewood method for primes (2007)

Venue: | IN: PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Green07generalisingthe,

author = {Ben Green},

title = {Generalising the Hardy-Littlewood method for primes},

booktitle = {IN: PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS},

year = {2007},

pages = {373--399},

publisher = {}

}

### OpenURL

### 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.