A potential analogue of Schinzel's hypothesis for polynomials with coefficients in Fq[t]

Abstract

The Schinzel hypothesis essentially claims that finitely many irreducible polynomials in one variable over Z simultaneously assume infinitely many prime values unless there is an obvious reason why this is impossible. We prove that under a restriction on the characteristic of the finite field Fq and a smoothness assumption, finitely many irreducible polynomials in one variable over the ring Fq[t] assume simultaneous prime values after a sufficiently large extension of the field of constants.

9 pages; minor improvements

Cited by in corpus (4)

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• Representing an element in F_q[t] as the sum of two irreducibles
• Probabilities of incidence between lines and a plane curve over finite fields
• Irreducible values of polynomials