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Computing ray class groups, conductors and discriminants

Authors: H. Cohen, F. Diaz y Diaz and M. Olivier
Journal: Math. Comp. 67 (1998), 773-795
MSC (1991): Primary 11R37, 11Y40
MathSciNet review: 1443117
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Abstract: We use the algorithmic computation of exact sequences of Abelian groups to compute the complete structure of $(\mathbb {Z}_{K}/\mathfrak {m})^{*}$ for an ideal $\mathfrak {m}$ of a number field $K$, as well as ray class groups of number fields, and conductors and discriminants of the corresponding Abelian extensions. As an application we give several number fields with discriminants less than previously known ones.

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Additional Information

H. Cohen
Affiliation: Laboratoire A2X, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France

F. Diaz y Diaz
Affiliation: Laboratoire A2X, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France

M. Olivier
Affiliation: Laboratoire A2X, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France

Keywords: Ray class groups, conductors, discriminants
Received by editor(s): February 19, 1996
Received by editor(s) in revised form: October 30, 1996
Article copyright: © Copyright 1998 American Mathematical Society