On computing discriminants of subfields of Q(zeta(pr))

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 calcu...

Full description

Bibliographic Details
Authors: Neto, TPDN, Interlando, J. C., Lopes, JOD
Format: article
Status:Published version
Publication Date:2002
Country:Brasil
Institution:Universidade Estadual Paulista (UNESP)
Repository:Repositório Institucional da UNESP
Language:English
OAI Identifier:oai:repositorio.unesp.br:11449/35981
Online Access:http://dx.doi.org/10.1006/jnth.2002.2796
http://hdl.handle.net/11449/35981
Access Level:Open access
Keyword:characters
conductors
Cyclotomic fields
discriminants of number fields
Hasse Theorem
Description
Summary: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 B.V. (USA).