Generators and irreducible polynomials over finite fields
HTML articles powered by AMS MathViewer
- by Daqing Wan PDF
- Math. Comp. 66 (1997), 1195-1212 Request permission
Abstract:
Weil’s character sum estimate is used to study the problem of constructing generators for the multiplicative group of a finite field. An application to the distribution of irreducible polynomials is given, which confirms an asymptotic version of a conjecture of Hansen-Mullen.References
- Eric Bach, James Driscoll, and Jeffrey Shallit, Factor refinement, J. Algorithms 15 (1993), no. 2, 199–222. MR 1231441, DOI 10.1006/jagm.1993.1038
- F. R. K. Chung, Diameters and eigenvalues, J. Amer. Math. Soc. 2 (1989), no. 2, 187–196. MR 965008, DOI 10.1090/S0894-0347-1989-0965008-X
- 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
- Gove W. Effinger and David R. Hayes, Additive number theory of polynomials over a finite field, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1143282
- W. B. Han, Some Applications of Character Sums in Finite Fields and Coding Theory, Ph.D. Dissertation, Sichuan University, 1994.
- 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
- Nicholas M. Katz, An estimate for character sums, J. Amer. Math. Soc. 2 (1989), no. 2, 197–200. MR 965007, DOI 10.1090/S0894-0347-1989-0965007-8
- H. W. Lenstra Jr., Finding isomorphisms between finite fields, Math. Comp. 56 (1991), no. 193, 329–347. MR 1052099, DOI 10.1090/S0025-5718-1991-1052099-2
- H. W. Lenstra Jr., Multiplicative groups generated by linear expressions, unpublished notes.
- H. W. Lenstra Jr. and R. J. Schoof, Primitive normal bases for finite fields, Math. Comp. 48 (1987), no. 177, 217–231. MR 866111, DOI 10.1090/S0025-5718-1987-0866111-3
- Wen-Ch’ing Winnie Li, Character sums and abelian Ramanujan graphs, J. Number Theory 41 (1992), no. 2, 199–217. With an appendix by Ke Qin Feng and the author. MR 1164798, DOI 10.1016/0022-314X(92)90120-E
- Victor Shoup, Searching for primitive roots in finite fields, Math. Comp. 58 (1992), no. 197, 369–380. MR 1106981, DOI 10.1090/S0025-5718-1992-1106981-9
- Igor E. Shparlinski, Computational and algorithmic problems in finite fields, Mathematics and its Applications (Soviet Series), vol. 88, Kluwer Academic Publishers Group, Dordrecht, 1992. MR 1249064, DOI 10.1007/978-94-011-1806-4
- Da Qing Wan, A $p$-adic lifting lemma and its applications to permutation polynomials, 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. 209–216. MR 1199834
- André Weil, Basic number theory, 3rd ed., Die Grundlehren der mathematischen Wissenschaften, Band 144, Springer-Verlag, New York-Berlin, 1974. MR 0427267, DOI 10.1007/978-3-642-61945-8
Additional Information
- Daqing Wan
- Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
- MR Author ID: 195077
- Email: wan@math.psu.edu
- Received by editor(s): December 8, 1995
- Received by editor(s) in revised form: May 8, 1996
- Additional Notes: This research was partially supported by NSF
- © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 1195-1212
- MSC (1991): Primary 11T24, 11T55
- DOI: https://doi.org/10.1090/S0025-5718-97-00835-1
- MathSciNet review: 1401947