Dynatomic Galois groups for a family of quadratic rational maps
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909074413584384 |
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| author | Krumm, David Lacy, Allan |
| author_facet | Krumm, David Lacy, Allan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05632 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynatomic Galois groups for a family of quadratic rational maps Krumm, David Lacy, Allan Number Theory Primary 37P05, Secondary 11S20, 11G30 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. |
| title | Dynatomic Galois groups for a family of quadratic rational maps |
| topic | Number Theory Primary 37P05, Secondary 11S20, 11G30 |
| url | https://arxiv.org/abs/2303.05632 |