Abstract: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 $\{1,\theta,\theta^2,\ldots,\theta^{N-1}\}$ is a basis for the ring of integers of ${\mathbb Q}(\theta)$, where $f(\theta)=0$. 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 $ab\ne 0$.
| Subjects: | Number Theory (math.NT) |
| Cite as: | arXiv:2605.25753 [math.NT] |
| (or arXiv:2605.25753v1 [math.NT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25753 arXiv-issued DOI via DataCite (pending registration) |
From: Lenny Jones Ph.D. [view email]
[v1]
Mon, 25 May 2026 12:04:28 UTC (10 KB)
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