Uniform distribution of the Steinitz invariants of quadratic and cubic extensions
Uniform distribution of the Steinitz invariants of quadratic and cubic extensions
复制标题
二次和三次扩张的斯坦尼茨不变量的均匀分布
DOI：
10.1112/s0010437x05001740
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发表时间：
2006
影响因子：
1.8
通讯作者：
David J. Wright
中科院分区：
文献类型：
--
作者：
A. Kable;David J. Wright
证明了当数域的三次扩张按其相关判别式的理想范数排序时，其Steinitz不变量在类群中均匀分布.即使通过在有限数量的位置指定其分裂类型来限制扩展，这仍然是正确的。同样的陈述也证明了二次扩张。
It is shown that the Steinitz invariants of the cubic extensions of a number field are uniformly distributed in the class group when the cubic extensions are ordered by the ideal norm of their relative discriminants. This remains true even if the extensions are restricted by specifying their splitting type at a finite number of places. The same statement is also proved for quadratic extensions.