Irreducible values of polynomials

Abstract

Schinzel's Hypothesis H is a general conjecture in number theory on prime values of polynomials that generalizes, e.g., the twin prime conjecture and Dirichlet's theorem on primes in arithmetic progression. We prove an arithmetic analog of this conjecture for polynomial rings over pseudo algebraically closed fields. This implies results over large finite fields. A main tool in the proof is an irreducibility theorems à la Hilbert.

The paper was shorten, some errors were corrected

References in corpus (3)

• On Pseudo Algebraically Closed Extensions of Fields
• A potential analogue of Schinzel's hypothesis for polynomials with coefficients in Fq[t]
• On PAC Extensions and Scaled Trace Forms