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Sifting for small primes from an arithmetic progression

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Abstract

In this work and its sister paper (Friedlander and Iwaniec (2023)), we give a new proof of the famous Linnik theorem bounding the least prime in an arithmetic progression. Using sieve machinery in both papers, we are able to dispense with the log-free zero density bounds and the repulsion property of exceptional zeros, two deep innovations begun by Linnik and relied on in earlier proofs.

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Acknowledgements

This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant No. A5123).

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada

    John B. Friedlander

  2. Department of Mathematics, Rutgers University, Piscataway, NJ, 08903, USA

    Henryk Iwaniec

Authors
  1. John B. Friedlander
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  2. Henryk Iwaniec
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Correspondence to John B. Friedlander.

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On the 50th Anniversary of Chen’s Goldbach Theorem

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Friedlander, J.B., Iwaniec, H. Sifting for small primes from an arithmetic progression. Sci. China Math. 66, 2715–2730 (2023). https://doi.org/10.1007/s11425-022-2123-2

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  • DOI: https://doi.org/10.1007/s11425-022-2123-2

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