The discriminant of subfields o f Q(ζ_(2r))

摘要

A formula for computing the discriminant of any number field K is contained in Q(ζ_(2r)), with r ≥ 3, is derived. The formula consists of two expressions, depending on whether K is cyclotomic or not. However, both expressions depend solely on m, the degree of K over Q, and they are derived from the Conductor-Discriminant Formula for Abelian extensions of Q.