TY - JOUR

T1 - The Green-Tao theorem on arithmetic progressions in the primes

T2 - An ergodic point of view

AU - Kra, Bryna

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2006/1

Y1 - 2006/1

N2 - 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.

AB - 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.

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U2 - 10.1090/S0273-0979-05-01086-4

DO - 10.1090/S0273-0979-05-01086-4

M3 - Article

AN - SCOPUS:32044462762

VL - 43

SP - 3

EP - 23

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

SN - 0273-0979

IS - 1

ER -