The difference between permutation polynomials over finite fields
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- by Stephen D. Cohen, Gary L. Mullen and Peter Jau-Shyong Shiue PDF
- Proc. Amer. Math. Soc. 123 (1995), 2011-2015 Request permission
Abstract:
Recently S. D. Cohen resolved a conjecture of Chowla and Zassenhaus (1968) in the affirmative by showing that, if $f(x)$ and $g(x)$ are integral polynomials of degree $n \geq 2$ and p is a prime exceeding ${({n^2} - 3n + 4)^2}$ for which f and g are both permutation polynomials of the finite field ${F_p}$, then their difference $h = f - g$ cannot be such that $h(x) = cx$ 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 ${F_p}$ and t is the degree of h, then $t \geq 3n/5$ and, provided $t \leq n - 3$, 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.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- 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