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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Tables of octic fields with a quartic subfield


Authors: H. Cohen, F. Diaz y Diaz and M. Olivier
Journal: Math. Comp. 68 (1999), 1701-1716
MSC (1991): Primary 11R37, 11Y40
Published electronically: February 24, 1999
MathSciNet review: 1642813
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Abstract: We describe the computation of extended tables of degree 8 fields with a quartic subfield, using class field theory. In particular we find the minimum discriminants for all signatures and for all the possible Galois groups. We also discuss some phenomena and statistics discovered while making the tables, such as the occurrence of 11 non-isomorphic number fields having the same discriminant, or several pairs of non-isomorphic number fields having the same Dedekind zeta function.


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Additional Information

H. Cohen
Affiliation: Laboratoire A2X, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France
Email: cohen@math.u-bordeaux.fr

F. Diaz y Diaz
Affiliation: Laboratoire A2X, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France
Email: diaz@math.u-bordeaux.fr

M. Olivier
Affiliation: Laboratoire A2X, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France
Email: olivier@math.u-bordeaux.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01074-1
PII: S 0025-5718(99)01074-1
Keywords: Class field theory, discriminant, number field
Received by editor(s): November 20, 1997
Published electronically: February 24, 1999
Article copyright: © Copyright 1999 American Mathematical Society