Number of irreducible polynomials and pairs of relatively prime polynomials in several variables over finite fields

被引：13

作者：

Hou, Xiang-dong ^{[1
]}

Mullen, Gary L. ^{[2
]}

机构：

[1] Univ S Florida, Dept Math, Tampa, FL 33620 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2009年 / 15卷 / 03期

关键词：

Finite field; Irreducible polynomial; Several variables; ARITHMETICAL FUNCTIONS;

D O I：

10.1016/j.ffa.2008.12.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 total degree and the vector degree, are considered. We show that the number of irreducibles call 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. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：304 / 331

页数：28

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