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arXiv · 2404.17869

Monogenic Cyclic Quartic Trinomials

Lenny Jones
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Abstract

A monic polynomial $f(x)\in {\mathbb Z}[x]$ of degree $N$ is called monogenic if $f(x)$ is irreducible over ${\mathbb Q}$ 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 brief note, we prove that there exist exactly three distinct monogenic trinomials of the form $x^4+bx^2+d$ whose Galois group is the cyclic group of order 4.

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Lenny Jones. 2024-04-27. Monogenic Cyclic Quartic Trinomials. https://arxiv.org/abs/2404.17869

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