Monogenic trinomials and class numbers of related quadratic fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908637025271808 |
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| author | Jones, Lenny |
| author_facet | Jones, Lenny |
| contents | We say that a monic polynomial $f(x)\in {\mathbb Z}[x]$ of degree $N\ge 2$ is monogenic if $f(x)$ is irreducible over ${\mathbb Q}$ and $\{1,θ,θ^2,\ldots ,θ^{N-1}\}$ is a basis for the ring of integers of ${\mathbb Q}(θ)$, where $f(θ)=0$. In this article, we investigate the divisibility of the class numbers of quadratic fields ${\mathbb Q}(\sqrtδ)$ for certain families of monogenic trinomials $f(x)=x^N+Ax+B$, where $δ\ne \pm 1$ is a squarefree divisor of the discriminant of $f(x)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20443 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monogenic trinomials and class numbers of related quadratic fields Jones, Lenny Number Theory We say that a monic polynomial $f(x)\in {\mathbb Z}[x]$ of degree $N\ge 2$ is monogenic if $f(x)$ is irreducible over ${\mathbb Q}$ and $\{1,θ,θ^2,\ldots ,θ^{N-1}\}$ is a basis for the ring of integers of ${\mathbb Q}(θ)$, where $f(θ)=0$. In this article, we investigate the divisibility of the class numbers of quadratic fields ${\mathbb Q}(\sqrtδ)$ for certain families of monogenic trinomials $f(x)=x^N+Ax+B$, where $δ\ne \pm 1$ is a squarefree divisor of the discriminant of $f(x)$. |
| title | Monogenic trinomials and class numbers of related quadratic fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.20443 |