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Imprimitive ninth-degree number fields with small discriminants. (English) Zbl 0819.11070

Known methods for computing algebraic number fields of small degree and small (absolute) discriminants were applied successfully up to degree 8 (for totally real fields). Considering imprimitive fields is somewhat easier. Consequently the authors compute tables of ninth degree fields of small discriminant which contain cubic subfields. They employ a theorem of J. Martinet [Théorie des Nombres, Sémin. Delange-Pilot- Poitou, Paris 1983-84, Prog. Math. 59, 147-179 (1985; Zbl 0567.12009)] to derive bounds for the coefficients of a generating cubic polynomial over a cubic subfield. The calculated tables contain a great deal of interesting data on a total of 1112 ninth degree number fields. These data are included by microfiche.
Reviewer: M.Pohst (Berlin)

MSC:

11Y40 Algebraic number theory computations
11R21 Other number fields
11-04 Software, source code, etc. for problems pertaining to number theory
11R16 Cubic and quartic extensions

Citations:

Zbl 0567.12009

Software:

KANT/KASH
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