Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields

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dc.creatorHou, Xiang-dong
dc.creatorMullen, Gary L.
dc.date2008-11-24
dc.date.accessioned2026-07-07T10:36:28Z
dc.date.available2026-07-07T10:36:28Z
dc.descriptionWe discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the {\em vector degree}, are considered. We show that the number of irreducibles can be computed recursively by degree and that the number of relatively prime pairs can be expressed in terms of the number of irreducibles. We also obtain asymptotic formulas for the number of irreducibles and the number of relatively prime pairs. The asymptotic formulas for the number of irreducibles generalize and improve several previous results by Carlitz, Cohen and Bodin.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/0811.3986
dc.identifierhttp://arxiv.org/abs/0811.3986
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180064
dc.subjectNumber Theory
dc.subject11T06
dc.titleNumber of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields
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