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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On some permutation polynomials over $ \mathbb{F}_q$ of the form $ x^r h(x^{(q-1)/d})$


Author: Michael E. Zieve
Journal: Proc. Amer. Math. Soc. 137 (2009), 2209-2216
MSC (2000): Primary 11T06
Published electronically: December 22, 2008
MathSciNet review: 2495253
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Abstract: Several recent papers have given criteria for certain polynomials to permute $ \mathbb{F}_q$, in terms of the periods of certain generalized Lucas sequences. We show that these results follow from a more general criterion which does not involve such sequences.


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Additional Information

Michael E. Zieve
Affiliation: Department of Mathematics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854
Email: zieve@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09767-0
PII: S 0002-9939(08)09767-0
Keywords: Permutation polynomial, finite field, binomial, Lucas sequence
Received by editor(s): September 16, 2008
Published electronically: December 22, 2008
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.