On computing discriminants of subfields of Q(ζpr)

[摘要] The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(Q(zeta(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(zeta(p)r), where p is an odd prime and r is a positive integer. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-10-01

[关键词] characters;conductors;cyclotomic fields;discriminants of number fields;Hasse Theorem