COUNTING IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS

被引：1

作者：

Wang, Qichun ^{[1
]}

Kan, Haibin ^{[1
]}

机构：

[1] Fudan Univ, Sch Comp Sci, Shanghai Key Lab Intelligent Informat Proc, Shanghai 200433, Peoples R China

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2010年 / 60卷 / 03期

关键词：

finite fields; distribution of irreducible polynomials; residue;

D O I：

10.1007/s10587-010-0055-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: pi(x) = q/q-1 x/log(q)x + q/(q-1)(2) x/log(q)(2)x + O(x/log(q)(3)x), x = q(n) -> infinity where pi(x) denotes the number of monic irreducible polynomials in F(q)[t] with norm <= x.

引用

页码：881 / 886

页数：6