论文标题
$ {\ mathbb q}的函数字段类似物中的类组关系
Class Group Relations in a Function Field Analogue of ${\mathbb Q}(ζ_p, \sqrt[p]{n})$
论文作者
论文摘要
对于奇数prime $ p $和多项式$ p（t）$，我们考虑扩展$ f $ $ k = {\ mathbb f} _p（t）$通过毗邻$ x^p+tx-p（t）$定义的。这样的字段是数字字段$ {\ mathbb q}（\ sqrt [p] {n}）$的函数字段模拟。我们证明了有关Galois关闭$ l $ f $的两个定理：对于某些组$ a $而言，其级别0分隔级组为$ a^{p-1} $，并且其班级是$（p-1 $ s $ f $ $ f $的$（p-1）$ - 与R. Schoof和T. Honda的结果相似，是$ f $的$ f $。
For an odd prime $p$ and polynomial $P(T)$, we consider the extension $F$ of $k={\mathbb F}_p(T)$ defined by adjoining a root of $x^p+Tx-P(T)$. Such a field is a function field analogue of the number field ${\mathbb Q}(\sqrt[p]{n})$. We prove two theorems about the Galois closure $L$ of $F$: that its degree-0 divisor class group is $A^{p-1}$ for some group $A$, and that its class number is the $(p-1)$-st power of the class number of $F$, in analogy with results of R. Schoof and T. Honda for number fields.
