Czechoslovak Mathematical Journal, first online, pp. 1-25


A higher rank Selberg sieve and applications

Akshaa Vatwani

Received August 2, 2016.   First published December 12, 2017.

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
Classification MSC:  11N05, 11N35, 11N36
DOI:  10.21136/CMJ.2017.0410-16

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Affiliations:   Akshaa Vatwani, Department of Mathematics and Statistics, Queen's University, 99 University Ave, Kingston, Ontario K7L3N6, Canada, e-mail: akshaa@mast.queensu.ca


 
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