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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Imprimitive ninth-degree number fields with small discriminants

Authors: F. Diaz y Diaz and M. Olivier
Journal: Math. Comp. 64 (1995), 305-321
MSC: Primary 11Y40; Secondary 11R21, 11R29, 11R32
MathSciNet review: 1260128
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Abstract: We present tables of ninth-degree nonprimitive (i.e., containing a cubic subfield) number fields. Each table corresponds to one signature, except for fields with signature (3,3), for which we give two different tables depending on the signature of the cubic subfield. Details related to the computation of the tables are given, as well as information about the CPU time used, the number of polynomials that we deal with, etc. For each field in the tables, we give its discriminant, the discriminant of its cubic subfields, the relative polynomial generating the field over one of its cubic subfields, the corresponding (irreducible) polynomial over $ \mathbb{Q}$, and the Galois group of the Galois closure. Fields having interesting properties are studied in more detail, especially those associated with sextic number fields having a class group divisible by 3.

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Keywords: Cubic fields, relative extensions, discriminant
Article copyright: © Copyright 1995 American Mathematical Society

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