On computing discriminants of subfields of ℚ (ζp r)
The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(ℚ(ζn)/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 calculatin...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2002 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/66977 |
| Acceso en línea: | http://dx.doi.org/10.1016/S0022-314X(02)92796-4 http://hdl.handle.net/11449/66977 |
| Access Level: | acceso abierto |
| Palabra clave: | Characters Conductors Cyclotomic fields Discriminants of number fields Hasse theorem |
| Sumario: | The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(ℚ(ζn)/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(ζpr), where p is an odd rime and r is a positive integer. © 2002 Elsevier Science USA. |
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