The Green-Tao theorem on arithmetic progressions in the primes: An ergodic point of view

Bryna Kra*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

A long-standing and almost folkloric conjecture is that the primes contain arbitrarily long arithmetic progressions. Until recently, the only progress on this conjecture was due to van der Corput, who showed in 1939 that there are infinitely many triples of primes in arithmetic progression. In an amazing fusion of methods from analytic number theory and ergodic theory, Ben Green and Terence Tao showed that for any positive integer k, there exist infinitely many arithmetic progressions of length k consisting only of prime numbers. This is an introduction to some of the ideas in the proof, concentrating on the connections to ergodic theory.

Original languageEnglish (US)
Pages (from-to)3-23
Number of pages21
JournalBulletin of the American Mathematical Society
Volume43
Issue number1
DOIs
StatePublished - Jan 2006

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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