论文标题
$ s_4 $ - 特定规范
$S_4$-quartics with Prescribed Norms
论文作者
论文摘要
给定一个数字字段$ k $和有限生成的子组$ \ Mathcal {a} \ subseteq k^*$，我们研究$ k $的$ s_4 $ Quartic-Quartic Extensions的分布，使得$ \ Mathcal {a} $的元素是规范。我们表明，这种扩展的密度是$ k $的每个地方所谓的“本地群众”的产物。在几乎所有情况下，我们都会明确地给出这些本地质量，并给出计算其余案例的算法。
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.
