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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 Kra2005
 B. Kra, "The GreenTao theorem on arithmetic progressions in the primes: an ergodic point of view," Bull. Amer. Math. Soc., 43:1 (2006) 323 (electronic). (http://dx.doi.org/10.1090/S0273097905010864) MR 2188173
Abstract:
A longstanding 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.
