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

Michael E. Zieve:
On some permutation polynomials over GF(q) of the form x^rh(x^(q-1)/d),
Proc. Amer. Math. Soc., 137 (2009), 2209–2216.

(Both the published version and the arXiv version are available online.)

Recent papers by Akbary–Wang and Akbary–Alaric–Wang give sufficient conditions for certain polynomials to permute 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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