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An Independent System of Units in Certain Algebraic Number Fields

Published online by Cambridge University Press:  20 November 2018

Claude Levesque*
Affiliation:
Université, Laval, Québec, Québec
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For Kn = Q(ω) a real algebraic number field of degree n over Q such that

with DN, dZ, d|D2, and D2 + 4d > 0, we proved in [5] (by using the approach of Halter-Koch and Stender [6]) that if

with

then

is an independent system of units of Kn.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Bernstein, L., Periodical continued fractions of degree n by Jacobi's algorithm, J. reine angew. Math. 213 (1964), 3138.Google Scholar
2. Bernstein, L., Representation of as a periodic continued fraction by JacobVs algorithm, Math. Nachr. 29 (1965), 179200.Google Scholar
3. Bernstein, L., Gaining units from units, Can. J. Math. 29 (1977), 93106.Google Scholar
4. Frei, G. and Levesque, C., On an independent system of units in the field where d|Dn, Abh. Math. Sem. Univ. Hamburg 51 (1980), 160163.Google Scholar
5. Frei, G. and Levesque, C., Independent systems of units in certain algebraic number fields, J. reine angew. Math. 311/312 (1979), 116144.Google Scholar
6. Halter-Koch, F. und Stender, H.-J., Unabhangige Einheiten für die Körper , Abh. Math. Sem. Univ. Hamburg 42 (1974), 3340.CrossRefGoogle Scholar
7. Stender, H.-J., Lösbare Gleichungen axn − byn = c und Grundeinheiten für einige algebraische Zahlkörper vom Grade n = 3, 4, 6, J. reine angew. Math. 290 (1977), 2462.Google Scholar