On Computing Discriminants of Subfields of [formula omitted](ζ pr)

Abstract

The conductor–discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal( Q (ζ n )/ Q ), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of Q (ζ p r ), where p is an odd prime and r is a positive integer.