Selberg’s sieve of irregular density
Acta Arithmetica MSC: Primary 11M20; Secondary 11N13, 11N35. DOI: 10.4064/aa220719-5-10 Opublikowany 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.