[1084] Écarts entre nombres premiers, et nombres premiers dans les progressions arithmétiques
Appears in collection : Bourbaki - Mars 2014
Y. Zhang and J. Maynard have recently revolutionized our knowledge of prime numbers. Zhang has first proved the existence of infinitely many pairs of primes at bounded distance from each other, and Maynard has not only improved his bound, but also proved the corresponding property for triples, quadruples, etc., of primes. These extraordinary results are based on the method discovered by Goldston, Pintz and Yıldırım for the study of gaps between primes. Zhang’s method is based on the proof of a statement concerning the distribution of primes in arithmetic progressions, beyond the reach of the Generalized Riemann Hypothesis, which is more adapted than those obtained by Fouvry, Bombieri, Friedlander and Iwaniec. Maynard’s work, on the other hand, is more elementary and involves only the Bombieri-Vinogradov Theorem. Both of these approaches will be presented.
[D'après Y. Zhang et J. Maynard]
