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.
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