Generalising the Hardy�Littlewood method for primes

• Autores: Benjamin Green
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé , Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 373-400
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • 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.