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Systemes Fondamentaux D'unites de Certains Corps de Degre 4 et de Degre 8 Sur Q

Published online by Cambridge University Press:  20 November 2018

Claude Levesque
Claude Levesque*
Affiliation:
Université Laval, Québec, Québec
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Lorsque Kn = Q(ω) est une extension algébrique de degré n sur Q telle que

avec D ∈ N, d ∈ Z, d|D2 et D2 + 4d > 0, nous avons prouvé [1] en utilisant certaines idées de Halter-Koch et Stender [2] que si

alors

est un système indépendant d'unités de Kn.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 5 , 01 October 1982 , pp. 1059 - 1090
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Frei, G. and Levesque, C., Independent systems of units in certain algebraic number fields, J. reine angew. Math. 311/312 (1979), 116–144./Google Scholar
2. F., Halter-Koch and H.-J., Stender, Unabhàngige Einheiten fur die Kôrper K = Q(n\/Dn ± d) mit d\Dn, Abh. Math. Sem. Univ. Hamburg 42 (1974), 33–40./Google Scholar
3. Kubota, T., Uber den bizyklischen biquadratischen Zahlkôrper, Nagoya Math. J. 10 (1956), 65–85./Google Scholar
4. Kuroda, S., Ûber die Klassenzahlen algebraischer Zahlkôrper, Nagoya Math. J. 1 (1950), 1–10./Google Scholar
5. H.-J., Stender, Lbsbare Gleichungen axn — byn — c und Grundeinheiten fur einige algebraische Zahlkôrper vom Grade n = 3, 4, 6, J. reine angew. Math. 290 (1977), 24–62./Google Scholar
6. H.-J., Stender, Verstilmmelte Grundeinheiten fur biquadratische und bikubische Zahlkôrper, Math. Ann. 232 (1978), 55–64./Google Scholar
7. Wada, H., On the class number and the unit group of certain algebraic number fields, Tokyo U., Fac. of Sc. J., Series 1, 13 (1966), 201–209./Google Scholar