English

Selberg's sieve of irregular density

Number Theory 2022-06-08 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2206.03479,
  title  = {Selberg's sieve of irregular density},
  author = {John Friedlander and Henryk Iwaniec},
  journal= {arXiv preprint arXiv:2206.03479},
  year   = {2022}
}

Comments

11 pages

R2 v1 2026-06-24T11:42:32.331Z