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Tables of octic fields with a quartic subfield. (English) Zbl 1036.11066

Summary: 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.
The method of computation given in the earlier paper [H. Cohen, F. Diaz y Diaz and M. Olivier, ibid. 67, 773–795 (1998; Zbl 0929.11064)] is used.

MSC:

11Y40 Algebraic number theory computations
11R37 Class field theory
11R21 Other number fields

Citations:

Zbl 0929.11064
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Full Text: DOI

References:

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