A Note on Abelian Monogenic Trinomials
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913161480765440 |
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| author | Jones, Lenny |
| author_facet | Jones, Lenny |
| contents | An abelian monogenic polynomial $f(x)\in {\mathbb Z}[x]$ is a monic polynomial of degree $N$ that is irreducible over ${\mathbb Q}$, such that the Galois group of $f(x)$ over ${\mathbb Q}$ is abelian, 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 determine all abelian monogenic trinomials of the form $x^{2n}+ax^{n}+b$, where $n,a,b\in {\mathbb Z}$ with $n\ge 1$ and $ab\ne 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25753 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Note on Abelian Monogenic Trinomials Jones, Lenny Number Theory An abelian monogenic polynomial $f(x)\in {\mathbb Z}[x]$ is a monic polynomial of degree $N$ that is irreducible over ${\mathbb Q}$, such that the Galois group of $f(x)$ over ${\mathbb Q}$ is abelian, 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 determine all abelian monogenic trinomials of the form $x^{2n}+ax^{n}+b$, where $n,a,b\in {\mathbb Z}$ with $n\ge 1$ and $ab\ne 0$. |
| title | A Note on Abelian Monogenic Trinomials |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.25753 |