Petits écarts entre les nombres premiers

Abstract : The aim of this report was to study in detail Maynard's article which was published in 2013. In this article, the author introduced a refinement of a method created by Goldston, Pintz and Yildirim based on sieve methods, called GPY sieve method, for studying prime k-tuples and small gaps between primes. This refinement avoids previous limitations of the method and allows to show that for each k, the prime k-tuples conjecture holds for a positive proportion of admissible k-tuples. In particular, lim infn(pn+m-pn) < [infinite] fot every integer m. In this article, it was also showed that lim infn(pn+1-pn) [below or equal] 600 and, if the Elliott-Halberstam conjecture if assumed, then lim infn(pn+1-pn) 6 12 and lim infn(pn+2- pn) [below or equal] 600.
Mots-clés : Crible Nombres premiers
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Master thesis
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http://docnum.univ-lorraine.fr/public/BUS_M_2015_FEUTRIE_DAVID.pdf
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David Feutrie. Petits écarts entre les nombres premiers. Mathématiques [math]. 2015. ⟨hal-01828891⟩

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