Iterates of Quadratics and Monogenicity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913380032315392 |
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| author | Smith, Hanson Wolske, Zack |
| author_facet | Smith, Hanson Wolske, Zack |
| contents | We investigate monogenicity and prime splitting in extensions generated by roots of iterated quadratic polynomials. Let $f(x)\in\mathbb{Z}[x]$ be an irreducible, monic, quadratic polynomial, and write $f^n(x)$ for the $n^{\text{th}}$ iterate. We obtain necessary and sufficient conditions for $f^n(x)$ to be monogenic for each $n$. We use this to construct multiple families where $f^n(x)$ is monogenic for every $n>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03629 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Iterates of Quadratics and Monogenicity Smith, Hanson Wolske, Zack Number Theory 11R04, 11R11, 11R21, 37P05 We investigate monogenicity and prime splitting in extensions generated by roots of iterated quadratic polynomials. Let $f(x)\in\mathbb{Z}[x]$ be an irreducible, monic, quadratic polynomial, and write $f^n(x)$ for the $n^{\text{th}}$ iterate. We obtain necessary and sufficient conditions for $f^n(x)$ to be monogenic for each $n$. We use this to construct multiple families where $f^n(x)$ is monogenic for every $n>0$. |
| title | Iterates of Quadratics and Monogenicity |
| topic | Number Theory 11R04, 11R11, 11R21, 37P05 |
| url | https://arxiv.org/abs/2406.03629 |