Czechoslovak Mathematical Journal

, Volume 68, Issue 1, pp 169–193 | Cite as

A higher rank Selberg sieve and applications

Article

Abstract

We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.

Keywords

Selberg sieve bounded gaps prime k-tuples 

MSC 2010

11N05 11N35 11N36 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsQueen’s UniversityKingston, OntarioCanada

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