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

Andreas O. Bender·Olivier Wittenberg
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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.

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Andreas O. Bender, Olivier Wittenberg. 2004-12-15. A potential analogue of Schinzel's hypothesis for polynomials with coefficients in Fq[t]. https://doi.org/10.1155/imrn.2005.2237

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