Dirichlet's Theorem for polynomial rings

Details Dirichlet's Theorem for polynomial rings Dirichlet's Theorem for polynomial rings

2006-12-27

arxiv.org/abs/math/0612801v3

Proc. Amer. Math. Soc. 137, 73-83 (2009)

Mathematics

Number Theory

final version

Scientific paper

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.

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