Obstructions to uniformity, and arithmetic patterns in the primes

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dc.creatorTao, Terence
dc.date2005-05-19
dc.date.accessioned2026-07-07T05:20:03Z
dc.date.available2026-07-07T05:20:03Z
dc.descriptionIn this expository article, we describe the recent approach, motivated by ergodic theory, towards detecting arithmetic patterns in the primes, and in particular establishing that the primes contain arbitrarily long arithmetic progressions. One of the driving philosophies is to identify precisely what the obstructions could be that prevent the primes (or any other set) from behaving ``randomly'', and then either show that the obstructions do not actually occur, or else convert the obstructions into usable structural information on the primes.
dc.description32 pages, no figures. Submitted, special edition of Quarterly J. Pure Appl. Math. in honour of John Coates
dc.identifierhttps://arxiv.org/abs/math/0505402
dc.identifierhttp://arxiv.org/abs/math/0505402
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75243
dc.subjectNumber Theory
dc.subject11N13, 11B25, 374A5
dc.titleObstructions to uniformity, and arithmetic patterns in the primes
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