Nombre d'extensions abéliennes sur Q

Artur Travesa

Journal de théorie des nombres de Bordeaux (1990)

  • Volume: 2, Issue: 2, page 413-423
  • ISSN: 1246-7405

Abstract

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The aim of this paper is to give the numbers of abelian number fields with given degree and ramification indices. We describe, also, an algorithm to compute all these fields.

How to cite

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Travesa, Artur. "Nombre d'extensions abéliennes sur Q." Journal de théorie des nombres de Bordeaux 2.2 (1990): 413-423. <http://eudml.org/doc/93524>.

@article{Travesa1990,
author = {Travesa, Artur},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {abelian fields; ramification; abelian number fields; cyclotomic extensions},
language = {fre},
number = {2},
pages = {413-423},
publisher = {Université Bordeaux I},
title = {Nombre d'extensions abéliennes sur Q},
url = {http://eudml.org/doc/93524},
volume = {2},
year = {1990},
}

TY - JOUR
AU - Travesa, Artur
TI - Nombre d'extensions abéliennes sur Q
JO - Journal de théorie des nombres de Bordeaux
PY - 1990
PB - Université Bordeaux I
VL - 2
IS - 2
SP - 413
EP - 423
LA - fre
KW - abelian fields; ramification; abelian number fields; cyclotomic extensions
UR - http://eudml.org/doc/93524
ER -

References

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  1. [Fa] Faltings, G., Wüstholz, G., et al., "Rational points," Seminar Bonn-Wuppertal 1983/84, Friedr. Vieweg & Sohm, 1984. 
  2. [Kr] Krasner, M., Nombre des extensions d'un degré donné d'un corps p-adique, C. R. Acad. Sc. Paris254, 255 (1962), 3470-3472, 224-226, 1682-1684, 2342-2344, 3095-3097. Voir aussi "Les Tendances Géométriques en Algèbre et Théorie des Nombres" dans Colloques Internationaux du C.N.R.S., 143 (1966), pp. 143-169. Zbl0117.02802
  3. [Sa] Šafarevič, I.R., Algebraic Number Fields, Amer. Math. Soc. Trans.31 (1963), 25-39. 
  4. [Se] Serre, J.-P., Une formule de masse pour les extensions totalement ramifiées de degré donné d'un corps local, C. R. Acad. Sc. Paris286 (1978), 1031-1036. Zbl0388.12005MR500361
  5. [Tr 1] Travesa, A., "Nombres d'extensions abelianes i les seves funcions generatrius," Thse, Universitat de Barcelona, 1987. 
  6. [Tr 2] Travesa, A., Generating functions for the numbers of abelian extensions of a local field, Proc. Amer. Math. Soc.108 (1990), 331-339. Zbl0695.12010MR1007513
  7. [vdW] van der Waerden, B.L., "Algebra," vol. 1, Frederick Ungar Pub. Co., New York, 1970. Zbl0137.25403MR263582
  8. [Wa] Washington, L.C., "Introduction to Cyclotomic Fields," GTM 83Springer-Verlag, New-York, 1982. Zbl0484.12001MR718674

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