Bulletin of the American Mathematical Society

The Green-Tao Theorem on arithmetic progressions in the primes: an ergodic point of view

Author(s): Bryna Kra
Journal: Bull. Amer. Math. Soc. 43 (2006), 3-23.
MSC (2000): Primary 11N13, 37A45, 11B25
Posted: October 6, 2005
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Abstract: A long-standing and almost folkloric conjecture is that the primes contain arbitrarily long arithmetic progressions. Until recently, the only prog- ress 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

, there exist infinitely many arithmetic progressions of length

consisting only of prime numbers. This is an introduction to some of the ideas in the proof, concentrating on the connections to ergodic theory.

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Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 11N13, 37A45, 11B25

Bryna Kra
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Rd., Evanston, Illinois 60208-2730
Email: kra@math.northwestern.edu

DOI: 10.1090/S0273-0979-05-01086-4
PII: S 0273-0979(05)01086-4
Received by editor(s): July 2005
Posted: October 6, 2005
Additional Notes: This article is an expanded version of a lecture presented January 7, 2005, at the AMS Special Session on Current Events, Joint Mathematics Meetings, Atlanta, GA. The author was partially supported by NSF grant DMS-0244994.
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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