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

Autor:	Hou, Xiang-dong, Mullen, Gary L.
Rok vydání:	2008
Předmět:	Mathematics - Number Theory 11T06
Druh dokumentu:	Working Paper
Popis:	We 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. Comment: 33 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0811.3986 Zobrazit plný text záznamu View this record from Arxiv