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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 and a smoothness assumption, finitely many irreducible polynomials in one variable over the ring F  q  [ t ] assume simultaneous prime values after a sufficiently large extension of the field of constants.

A potential analogue of Schinzel's hypothesis for polynomialswith coefficients in F q [ t ]