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arXiv · 2602.12213

On the dynamical Galois group of certain affine polynomials in positive characteristic

Andrea Ferraguti·Guido Maria Lido
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Abstract

We use explicit class field theory of rational function fields to prove a dynamical criterion for a polynomial of the form $x^{p^r}+ax+b$ over a field of characteristic $p$ to have dynamical Galois group as large as possible. When $p=2$ and $r=1$ this yields an analogue in characteristic $2$ of the celebrated criterion of Stoll for quadratic polynomials over fields of characteristic not $2$.

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Andrea Ferraguti, Guido Maria Lido. 2026-02-12. On the dynamical Galois group of certain affine polynomials in positive characteristic. https://arxiv.org/abs/2602.12213

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