The difference between permutation polynomials over finite fields
Authors:
Stephen D. Cohen, Gary L. Mullen and Peter Jau-Shyong Shiue
Journal:
Proc. Amer. Math. Soc. 123 (1995), 2011-2015
MSC:
Primary 11T06
DOI:
https://doi.org/10.1090/S0002-9939-1995-1196163-1
MathSciNet review:
1196163
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Abstract | References | Similar Articles | Additional Information
Abstract: Recently S. D. Cohen resolved a conjecture of Chowla and Zassenhaus (1968) in the affirmative by showing that, if and
are integral polynomials of degree
and p is a prime exceeding
for which f and g are both permutation polynomials of the finite field
, then their difference
cannot be such that
for some integer c not divisible by p. In this note we provide a significant generalization by proving that, if h is not a constant in
and t is the degree of h, then
and, provided
, t and n are not relatively prime. In a sense this measures the isolation of permutation polynomials of the same degree over large finite prime fields.
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- [2] S. D. Cohen, Proof of a conjecture of Chowla and Zassenhaus on permutation polynomials, Canad. Math. Bull. 33 (1990), 230-234. MR 1060378 (91g:11146)
- [3] M. Fried, On a conjecture of Schur, Michigan Math. J. 17 (1970), 41-55. MR 0257033 (41:1688)
- [4] L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley-Interscience, New York, 1974. MR 0419394 (54:7415)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1995-1196163-1
Keywords:
Finite field,
permutation polynomial
Article copyright:
© Copyright 1995
American Mathematical Society