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Selberg’s sieve of irregular density

Volume 209 / 2023

J. B. Friedlander, H. Iwaniec Acta Arithmetica 209 (2023), 385-396 MSC: Primary 11M20; Secondary 11N13, 11N35. DOI: 10.4064/aa220719-5-10 Published online: 27 October 2022


We study certain aspects of the Selberg sieve, in particular when sifting by rather thin sets of primes. We derive new results for the lower bound sieve suited especially for this setup and we apply them in particular to give a new sieve-propelled proof of Linnik’s theorem on the least prime in an arithmetic progression in the case of the presence of exceptional zeros.


  • J. B. FriedlanderDepartment of Mathematics
    University of Toronto
    Toronto, Ontario M5S 2E4, Canada
  • H. IwaniecDepartment of Mathematics
    Rutgers University
    Piscataway, NJ 08903, USA

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