Distribution of irreducible polynomials of small degrees over finite fields

Kie H. Ham, Gary L. Mullen

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)337-341
Number of pages5
JournalMathematics of Computation
Volume67
Issue number221
DOIs
StatePublished - Jan 1998

Fingerprint

Irreducible polynomial
Galois field
Polynomials
Verify

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{ad29df7b678f4f9da42b925e83919e8e,
title = "Distribution of irreducible polynomials of small degrees over finite fields",
abstract = "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.",
author = "Ham, {Kie H.} and Mullen, {Gary L.}",
year = "1998",
month = "1",
doi = "10.1090/S0025-5718-98-00904-1",
language = "English (US)",
volume = "67",
pages = "337--341",
journal = "Mathematics of Computation",
issn = "0025-5718",
publisher = "American Mathematical Society",
number = "221",

}

Distribution of irreducible polynomials of small degrees over finite fields. / Ham, Kie H.; Mullen, Gary L.

In: Mathematics of Computation, Vol. 67, No. 221, 01.1998, p. 337-341.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Distribution of irreducible polynomials of small degrees over finite fields

AU - Ham, Kie H.

AU - Mullen, Gary L.

PY - 1998/1

Y1 - 1998/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032329918&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032329918&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-98-00904-1

DO - 10.1090/S0025-5718-98-00904-1

M3 - Article

AN - SCOPUS:0032329918

VL - 67

SP - 337

EP - 341

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 221

ER -