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A higher rank Selberg sieve and applications

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, 99 University Ave, Kingston, Ontario, K7L3N6, Canada

    Akshaa Vatwani

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  1. Akshaa Vatwani
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Correspondence to Akshaa Vatwani.

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Research partially supported by an Ontario Graduate Scholarship.

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Vatwani, A. A higher rank Selberg sieve and applications. Czech Math J 68, 169–193 (2018). https://doi.org/10.21136/CMJ.2017.0410-16

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  • DOI: https://doi.org/10.21136/CMJ.2017.0410-16

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