Distribution of irreducible polynomials of small degrees over finite fields

被引：21

作者：

Ham, KH ^{[1
]}

Mullen, GL ^{[1
]}

机构：

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

来源：

MATHEMATICS OF COMPUTATION | 1998年 / 67卷 / 221期

关键词：

D O I：

10.1090/S0025-5718-98-00904-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

D. Wan very recently proved an asymptotic version of a conjecture of Hansen and Mullen concerning the distribution of irreducible polynomials over finite fields. In this note we prove that the conjecture is true in general by using machine calculation to verify the open cases remaining after Wan's work.

引用

页码：337 / 341

页数：5

共 50 条

[21] A correspondence of certain irreducible polynomials over finite fields
Kim, Kitae
Yie, Ikkwon
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (02) : 384 - 395
[22] The Construction and Determination of Irreducible Polynomials Over Finite Fields
Song, Yun
Li, Zhihui
[J]. ADVANCES IN SWARM INTELLIGENCE, ICSI 2016, PT II, 2016, 9713 : 618 - 624
[23] Fast construction of irreducible polynomials over finite fields
Couveignes, Jean-Marc
Lercier, Reynald
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2013, 194 (01) : 77 - 105
[24] Polynomials over finite fields free from large and small degree irreducible factors
Garefalakis, T
Panario, D
[J]. JOURNAL OF ALGORITHMS, 2002, 44 (01) : 98 - 120
[25] Irreducible compositions of polynomials over finite fields of even characteristic
Mehrabi, Saeid
Kyuregyan, Melsik K.
[J]. APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2012, 23 (5-6) : 207 - 220
[26] A new direction on constructing irreducible polynomials over finite fields
Cheng, Kaimin
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2024, 95
[27] Constructions of irreducible polynomials over finite fields with even characteristic
P. L. Sharma
Shalini Ashima
Mansi Gupta
Sushil Harish
[J]. Indian Journal of Pure and Applied Mathematics, 2023, 54 : 734 - 742
[28] GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS
Ahn, Youngwoo
Kim, Kitae
[J]. KOREAN JOURNAL OF MATHEMATICS, 2011, 19 (03): : 263 - 272
[29] Irreducible compositions of polynomials over finite fields of even characteristic
Saeid Mehrabi
Melsik K. Kyuregyan
[J]. Applicable Algebra in Engineering, Communication and Computing, 2012, 23 : 207 - 220
[30] OBTAINING SPECIFIED IRREDUCIBLE POLYNOMIALS OVER FINITE-FIELDS
GOLOMB, SW
[J]. SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1980, 1 (04): : 411 - 418

← 1 2 3 4 5 →