On Computing Discriminants of Subfields of image(ζpr) Original Research Article

The conductor–discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(image(ζn)/image), 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 image(ζpr), where p is an odd prime and r is a positive integer.