Dirichlet's Theorem for polynomial rings
Number Theory
2009-07-16 v3
Abstract
We prove Dirichlet's theorem for polynomial rings: Let F be a pseudo algebraically closed field. Then for all relatively prime polynomials a(X), b(X)\in F[X] and for every sufficiently large positive integer n there exist infinitely many polynomials c(X)\in F[X] such that a(X) + b(X)c(X) is irreducible of degree n, provided that F has a separable extension of degree n.
Cite
@article{arxiv.math/0612801,
title = {Dirichlet's Theorem for polynomial rings},
author = {L. Bary-Soroker},
journal= {arXiv preprint arXiv:math/0612801},
year = {2009}
}
Comments
final version