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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.14819 |
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Table of Contents:
- For a prime $p$ and $p$-power $q$, let $f(x)\in\mathbb{F}_q[x]$ with $\textrm{deg}\ f$ coprime to $p$. As $λ$ varies in $\overline{\mathbb{F}_p^\times}$, Wan has conjectured that the $p$-adic Newton polygon of the corresponding Artin-Schreier curve given by $λf$ is constant. That is, \[ \textrm{NP}(f) = \textrm{NP}(λf). \] In this paper, we prove this conjecture when $λ\in\mathbb{F}_p^\times$ and provide a detailed counterexample showing it is false in general.