We describe some of the machinery behind recent progress in establishing infinitely many arithmetic progressions of length k in various sets of integers, in particular in arbitrary dense subsets of the integers, and in the primes.
@article{urn:eudml:doc:41790,
title = {Arithmetic progressions and the primes.},
journal = {Collectanea Mathematica},
volume = {57},
year = {2006},
pages = {37-88},
zbl = {1109.11043},
mrnumber = {MR2264205},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41790}
}
Tao, Terence. Arithmetic progressions and the primes.. Collectanea Mathematica, Tome 57 (2006) pp. 37-88. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41790/