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...
| Authors: | , , |
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| 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 |
| 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). |
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