Distribution of irreducible polynomials of small degrees over finite fields
HTML articles powered by AMS MathViewer
- by Kie H. Ham and Gary L. Mullen PDF
- Math. Comp. 67 (1998), 337-341 Request permission
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.References
- Stephen D. Cohen, Primitive elements and polynomials with arbitrary trace, Discrete Math. 83 (1990), no. 1, 1–7. MR 1065680, DOI 10.1016/0012-365X(90)90215-4
- Stephen D. Cohen, Primitive elements and polynomials: existence results, Finite fields, coding theory, and advances in communications and computing (Las Vegas, NV, 1991) Lecture Notes in Pure and Appl. Math., vol. 141, Dekker, New York, 1993, pp. 43–55. MR 1199821
- Wen Bao Han, The coefficients of primitive polynomials over finite fields, Math. Comp. 65 (1996), no. 213, 331–340. MR 1320895, DOI 10.1090/S0025-5718-96-00663-1
- Tom Hansen and Gary L. Mullen, Primitive polynomials over finite fields, Math. Comp. 59 (1992), no. 200, 639–643, S47–S50. MR 1134730, DOI 10.1090/S0025-5718-1992-1134730-7
- Rudolf Lidl and Harald Niederreiter, Finite fields, Encyclopedia of Mathematics and its Applications, vol. 20, Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. With a foreword by P. M. Cohn. MR 746963
- D. Wan, Generators and irreducible polynomials over finite fields, Math. Comp. 66 (1997), 1195–1212.
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
- Received by editor(s): May 20, 1996
- Received by editor(s) in revised form: October 7, 1996
- © Copyright 1998 American Mathematical Society
- 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