Last updated
2021-11-11T23:27:46.943+00:00
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.
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.
Symplectic ID
398493
Download URL
http://arxiv.org/abs/math/0601211v1
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Publication type
Journal Article
Publication date
10 Jan 2006