In the mid 80’s Conner and Perlis showed that for cyclic number fields of prime degree p the isometry class of integral trace is completely determined by the discriminant. Here we generalize their result to tame cyclic number fields of arbitrary degree. Furthermore, for such fields, we give an explicit description of a Gram matrix of the integral trace in terms of the discriminant of the field.

中文翻译：

---

循环数域上的跟踪表

在 80 年代中期，Conner 和 Perlis 表明，对于素数为p的循环数域，积分迹的等距类完全由判别式决定。在这里，我们将他们的结果推广到驯服任意程度的循环数场。此外，对于这些场，我们根据场的判别式给出了积分迹的 Gram 矩阵的明确描述。