Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897076 | Journal of Number Theory | 2018 | 22 Pages |
Abstract
We improve Irving's method of the double-sieve [7] by using the DHR sieve. By extending the upper and lower bound sieve functions into their respective non-elementary ranges, we are able to make improvements on the previous records on the number of prime factors of irreducible polynomials at prime arguments. In particular, we prove that irreducible quadratics over Z satisfying necessary local conditions are P4 infinitely often.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
P.-H. Kao,