Corps sextiques primitifs
Annales de l'Institut Fourier, Volume 40 (1990) no. 4, pp. 757-767.

We describe four tables of primitive sextic fields (one for each signature). The tables provide for each field, the discriminant, the Galois group of the Galois closure and a polynomial which defines the sextic field.

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 polynôme définissant le corps.

@article{AIF_1990__40_4_757_0,
     author = {Olivier, Michel},
     title = {Corps sextiques primitifs},
     journal = {Annales de l'Institut Fourier},
     pages = {757--767},
     publisher = {Institut Fourier},
     volume = {40},
     number = {4},
     year = {1990},
     doi = {10.5802/aif.1233},
     zbl = {0734.11054},
     mrnumber = {92a:11123},
     language = {fr},
     url = {http://archive.numdam.org/articles/10.5802/aif.1233/}
}
TY  - JOUR
AU  - Olivier, Michel
TI  - Corps sextiques primitifs
JO  - Annales de l'Institut Fourier
PY  - 1990
DA  - 1990///
SP  - 757
EP  - 767
VL  - 40
IS  - 4
PB  - Institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.1233/
UR  - https://zbmath.org/?q=an%3A0734.11054
UR  - https://www.ams.org/mathscinet-getitem?mr=92a:11123
UR  - https://doi.org/10.5802/aif.1233
DO  - 10.5802/aif.1233
LA  - fr
ID  - AIF_1990__40_4_757_0
ER  - 
%0 Journal Article
%A Olivier, Michel
%T Corps sextiques primitifs
%J Annales de l'Institut Fourier
%D 1990
%P 757-767
%V 40
%N 4
%I Institut Fourier
%U https://doi.org/10.5802/aif.1233
%R 10.5802/aif.1233
%G fr
%F AIF_1990__40_4_757_0
Olivier, Michel. Corps sextiques primitifs. Annales de l'Institut Fourier, Volume 40 (1990) no. 4, pp. 757-767. doi : 10.5802/aif.1233. http://archive.numdam.org/articles/10.5802/aif.1233/

[1] A.-M. Bergé, J. Martinet et M. Olivier, The computation of sextic fields with a quadratic subfield, Math. Comp., 54 (1990), 869-884. | MR | Zbl

[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

[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. | MR | Zbl

[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. | MR | Zbl

[6] J. Martinet, Méthodes géométriques dans la recherche des petits discriminants, Progress in Mathematics, 59 (1985), 147-179, Birkhäuser. | MR | Zbl

[7] M. Olivier, The computation of sextic fields with a cubic subfield and no quadratic subfield, Math. Comp. (à paraître). | Zbl

[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. | MR | Zbl

[9] R. P. Stauduhar, The determination of Galois groups, Math. Comp., 27 (1973), 981-996. | MR | Zbl

Cited by Sources: