Mathematics of Computation

Author(s): Kie H. Ham; Gary L. Mullen.
Journal: Math. Comp. 67 (1998), 337-341.
MSC (1991): Primary 11T06
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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: $\underline{Finite Fields, Coding}$
$\underline{Theory,}$ $\underline{and Advances in Communications and Computing}$ , (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, $\underline{Finite Fields}$ , 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

Kie H. Ham
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: csh102@psu.edu

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