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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

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


Author: Bryna Kra
Journal: Bull. Amer. Math. Soc. 43 (2006), 3-23
MSC (2000): Primary 11N13, 37A45, 11B25
Published electronically: October 6, 2005
MathSciNet review: 2188173
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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 $ 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.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0273-0979-05-01086-4
PII: S 0273-0979(05)01086-4
Received by editor(s): July 1, 2005
Published electronically: 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.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.