Primes in arithmetic progressions
Étienne Fouvry,Henryk Iwaniec +1 more
About: This article is published in Acta Arithmetica. The article was published on 01 Jan 1983. and is currently open access. The article focuses on the topics: Problems involving arithmetic progressions & Dirichlet's theorem on arithmetic progressions.
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Bounded gaps between primes
Abstract: It is proved that
lim inf n?8 (p n+1 -p n )<7×10 7 , where p n is the n -th prime.
Our method is a refinement of the recent work of Goldston, Pintz and Yildirim on the small gaps between consecutive primes. A major ingredient of the proof is a stronger version of the Bombieri-Vinogradov theorem that is applicable when the moduli are free from large prime divisors only, but it is adequate for our purpose
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A remark on Artin's conjecture
TL;DR: In this article, a finite set S such that for some a e S, a is a pr imi t ive roo t ( m o d p ) for an infini ty o f p r i m e s p.
New equidistribution estimates of Zhang type
Wouter Castryck,Étienne Fouvry,Gergely Harcos,Emmanuel Kowalski,Philippe Michel,Paul D. Nelson,E. Paldi,János Pintz,Andrew V. Sutherland,Terence Tao,Xiao-Feng Xie +10 more
TL;DR: For arithmetic progressions to large smooth squarefree moduli, with respect to congruence classes obeying Chinese remainder theorem conditions, the authors obtained an exponent of distribution 1/2 + 7/300.