论文标题
在纯正学位数字字段的形状上
On the shapes of pure prime degree number fields
论文作者
论文摘要
对于$ p $ prime和$ \ ell = \ frac {p-1} {2} $，我们表明，纯质学位数字字段的形状位于形状空间的两个$ \ ell $ - 维子空间之一，以及两个子空间中的哪个是由$ p $ ramifies wildly willly of lightilly所决定的。当通过绝对判别剂订购字段时，我们表明这些形状在这些子空间上是正则化的。我们还表明，这种形状是纯正学位领域家族中完全不变的。这扩展了[HAR17]中的Harron的结果，后者在纯立方数字字段中研究了形状。此外，我们将纯Prime Number字段的语句转换为有关Frobenius编号字段的语句，$ f_p = C_P \ rtimes C_ {P-1} $，带有固定的分辨率字段。具体来说，我们表明这项研究等于对具有固定解析字段$ \ Mathbb {q}（ζ_P）$的$ f_p $ -Number字段的研究。
For $p$ prime and $\ell = \frac{p-1}{2}$, we show that the shapes of pure prime degree number fields lie on one of two $\ell$-dimensional subspaces of the space of shapes, and which of the two subspaces is dictated by whether or not $p$ ramifies wildly. When the fields are ordered by absolute discriminant we show that the shapes are equidistributed, in a regularized sense, on these subspaces. We also show that the shape is a complete invariant within the family of pure prime degree fields. This extends the results of Harron, in [Har17], who studied shapes in the case of pure cubic number fields. Furthermore we translate the statements of pure prime degree number fields to statements about Frobenius number fields, $F_p = C_p\rtimes C_{p-1}$, with a fixed resolvent field. Specifically we show that this study is equivalent to the study of $F_p$-number fields with fixed resolvent field $\mathbb{Q}(ζ_p)$.
