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arXiv · 2210.06992

$S_4$-quartics with Prescribed Norms

Sebastian Monnet
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Abstract

Given a number field $k$ and a finitely generated subgroup $\mathcal{A} \subseteq k^*$, we study the distribution of $S_4$-quartic extensions of $k$ such that the elements of $\mathcal{A}$ are norms. We show that the density of such extensions is the product of so-called "local masses" at every place of $k$. We give these local masses explicitly in almost all cases and give an algorithm for computing the remaining cases.

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Sebastian Monnet. 2022-10-13. $S_4$-quartics with Prescribed Norms. https://arxiv.org/abs/2210.06992

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