Uniform distribution of the Steinitz invariants of quadratic and cubic extensions

[摘要] 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.

[学科分类] 数学（综合）