On some permutation polynomials over 𝔽_{𝕢} of the form 𝕩^{𝕣}𝕙(𝕩^{(𝕢-1)/𝕕})

Zieve, Michael

doi:10.1090/S0002-9939-08-09767-0

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

Proc. Amer. Math. Soc. 137 (2009), 2209-2216 Request permission

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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