Sifting for small primes from an arithmetic progression

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 o...

Full description

Saved in:
Bibliographic Details
Published in:Science China. Mathematics 2023-12, Vol.66 (12), p.2715-2730
Main Authors: Friedlander, John B., Iwaniec, Henryk
Format: Article
Language:English
Subjects:
Applications of Mathematics
Arithmetic
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-022-2123-2