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Olivier, Michel

Corps sextiques primitifs. (Primitive sextic fields). (French) Zbl 0734.11054

Ann. Inst. Fourier 40, No. 4, 757-767 (1990).
Nous décrivons quatre tables de corps sextiques primitifs (une par signature). Les tables fournissent pour chaque corps, le discriminant, le groupe de Galois de la clôture galoisienne et un polynome définissant le corps.
Reviewer: M.Olivier (Bordeaux)

Cited in 1 Review
Cited in 7 Documents

MSC:

11R21 Other number fields
11Y40 Algebraic number theory computations
11R29 Class numbers, class groups, discriminants
11-04 Software, source code, etc. for problems pertaining to number theory

Keywords:

sextic fields; discriminant; defining polynomials; Galois group of Galois closure

Citations:

Zbl 0719.11088; Zbl 0709.11056; Zbl 0726.11081
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\textit{M. Olivier}, Ann. Inst. Fourier 40, No. 4, 757--767 (1990; Zbl 0734.11054)
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References:

[1] A.-M. BERGÉ, J. MARTINET et M. OLIVIER, The computation of sextic fields with a quadratic subfield, Math. Comp., 54 (1990), 869-884. · Zbl 0709.11056
[2] B. J. BIRCH et W. KUYK, éd., Modular functions of one variable IV, dit “Anvers IV”, Lectures Notes 476 (1975), Springer-Verlag, Heidelberg. · Zbl 0315.14014
[3] A. BRUMER, Exercices diédraux et courbes à multiplications réelles, Actes du Séminaire de théorie des nombres de Paris (1989/1990), Birkhäuser, Boston, à paraître.
[4] G. BUTLER and J. MCKAY, The transitive groups of degree up to eleven, Comm. Alg., 11 (1983), 863-911. · Zbl 0518.20003
[5] F. DIAZ Y DIAZ, Discriminant minimal et petits discriminants des corps de nombres de degré 7 avec 5 places réelles, J. London Math. Soc., 38 (1988), 33-46. · Zbl 0653.12003
[6] J. MARTINET, Méthodes géométriques dans la recherche des petits discriminants, Progress in Mathematics, 59 (1985), 147-179, Birkhäuser. · Zbl 0567.12009
[7] M. OLIVIER, The computation of sextic fields with a cubic subfield and no quadratic subfield, Math. Comp. (à paraître). · Zbl 0746.11041
[8] M. POHST, On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields, J. Number Theory, 14 (1982), 99-117. · Zbl 0478.12005
[9] R. P. STAUDUHAR, The determination of Galois groups, Math. Comp., 27 (1973), 981-996. · Zbl 0282.12004
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