Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Tables of octic fields with a quartic subfield

Author(s): H. Cohen; F. Diaz y Diaz; M. Olivier.
Journal: Math. Comp. 68 (1999), 1701-1716.
MSC (1991): Primary 11R37, 11Y40
Posted: 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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