Distribution of irreducible polynomials

of small degrees over finite fields

Authors:
Kie H. Ham and Gary L. Mullen

Journal:
Math. Comp. **67** (1998), 337-341

MSC (1991):
Primary 11T06

DOI:
https://doi.org/10.1090/S0025-5718-98-00904-1

MathSciNet review:
1434940

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Abstract | References | Similar Articles | Additional Information

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.

**1.**S. D. Cohen,*Primitive elements and polynomials with arbitrary trace*, Discrete Math.**83**(1990), 1-7. MR**91h:11143****2.**S. D. Cohen, Primitive elements and polynomials: existence results, In:

, (G. L. Mullen and P. J.-S. Shiue, Eds.), Lect. Notes in Pure & Appl. Math., Vol. 141(1993), Marcel Dekker, New York, pp. 43-55. MR**93k:11113****3.**W. B. Han,*The coefficients of primitive polynomials over finite fields*, Math. Comp.**65**(1996), 331-340. MR**96d:11128****4.**T. Hansen and G. L. Mullen,*Primitive polynomials over finite fields*, Math. Comp.**59**(1992), 639-643; Supplement S47-S50. MR**93a:11101****5.**R. Lidl and H. Niederreiter, , Encyclo. Math. Appl., Vol. 20, Addison-Wesley, Reading, MA, 1983 (Now distributed by Camb. Univ. Press). MR**86c:11106****6.**D. Wan,*Generators and irreducible polynomials over finite fields*, Math. Comp.**66**(1997), 1195-1212. CMP**96:16**

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Additional Information

**Kie H. Ham**

Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802

Email:
csh102@psu.edu

**Gary L. Mullen**

Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802

Email:
mullen@math.psu.edu

DOI:
https://doi.org/10.1090/S0025-5718-98-00904-1

Received by editor(s):
May 20, 1996

Received by editor(s) in revised form:
October 7, 1996

Article copyright:
© Copyright 1998
American Mathematical Society