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arXiv · 2303.05632

Dynatomic Galois groups for a family of quadratic rational maps

David Krumm·Allan Lacy
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Abstract

For every nonconstant rational function $ϕ\in\mathbb{Q}(x)$, the Galois groups of the dynatomic polynomials of $ϕ$ encode various properties of $ϕ$ that are of interest in the subject of arithmetic dynamics. We study here the structure of these Galois groups as $ϕ$ varies in a particular one-parameter family of maps, namely the quadratic rational maps having a critical point of period 2. In particular, we provide explicit descriptions of the third and fourth dynatomic Galois groups for maps in this family.

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David Krumm, Allan Lacy. 2024-01-16. Dynatomic Galois groups for a family of quadratic rational maps. https://arxiv.org/abs/2303.05632

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