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arXiv · 1807.05495

Iteration of Polynomials $AX^d+C$ Over Finite Fields

Rufei Ren
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Abstract

For a polynomial $f(X)=AX^d+C \in \mathbb{F}_p[X]$ with $A\neq 0$ and $d\geq 2$, we prove that if $d\;|\;p-1$ and $f^i(0)\neq f^j(0)$ for $0\leq i<j\leq N$, then $\#f^N(\mathbb{F}_p) \sim \frac{2p}{(d-1)N},$ where $f^N$ is the $N$-th iteration of $f$.

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Rufei Ren. 2020-04-20. Iteration of Polynomials $AX^d+C$ Over Finite Fields. https://doi.org/10.1016/j.jnt.2020.03.009

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