On the dynamical Galois group of certain affine polynomials in positive characteristic
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917270886809600 |
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| author | Ferraguti, Andrea Lido, Guido Maria |
| author_facet | Ferraguti, Andrea Lido, Guido Maria |
| contents | 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 $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12213 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the dynamical Galois group of certain affine polynomials in positive characteristic Ferraguti, Andrea Lido, Guido Maria Number Theory 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 $2$. |
| title | On the dynamical Galois group of certain affine polynomials in positive characteristic |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.12213 |