Corps sextiques primitifs

Michel Olivier

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 4, page 757-767
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Olivier, Michel. "Corps sextiques primitifs." Annales de l'institut Fourier 40.4 (1990): 757-767. <http://eudml.org/doc/74897>.

@article{Olivier1990,
abstract = {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.},
author = {Olivier, Michel},
journal = {Annales de l'institut Fourier},
keywords = {sextic fields; discriminant; defining polynomials; Galois group of Galois closure},
language = {fre},
number = {4},
pages = {757-767},
publisher = {Association des Annales de l'Institut Fourier},
title = {Corps sextiques primitifs},
url = {http://eudml.org/doc/74897},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Olivier, Michel
TI - Corps sextiques primitifs
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 4
SP - 757
EP - 767
AB - 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.
LA - fre
KW - sextic fields; discriminant; defining polynomials; Galois group of Galois closure
UR - http://eudml.org/doc/74897
ER -

References

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  1. [1] A.-M. BERGÉ, J. MARTINET et M. OLIVIER, The computation of sextic fields with a quadratic subfield, Math. Comp., 54 (1990), 869-884. Zbl0709.11056MR90k:11169
  2. [2] B. J. BIRCH et W. KUYK, éd., Modular Functions of One Variable IV, dit "Anvers IV", Lectures Notes 476 (1975), Springer-Verlag, Heidelberg. Zbl0315.14014
  3. [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. [4] G. BUTLER and J. MCKAY, The transitive groups of degree up to eleven, Comm. Alg., 11 (1983), 863-911. Zbl0518.20003MR84f:20005
  5. [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. Zbl0653.12003MR90b:11113
  6. [6] J. MARTINET, Méthodes géométriques dans la recherche des petits discriminants, Progress in Mathematics, 59 (1985), 147-179, Birkhäuser. Zbl0567.12009MR88h:11083
  7. [7] M. OLIVIER, The computation of sextic fields with a cubic subfield and no quadratic subfield, Math. Comp. (à paraître). Zbl0746.11041
  8. [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. Zbl0478.12005MR83g:12009
  9. [9] R. P. STAUDUHAR, The determination of Galois groups, Math. Comp., 27 (1973), 981-996. Zbl0282.12004MR48 #6054

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