Geodesic
An Independent System of Units in Certain Algebraic Number Fields
Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 644-663

Voir la notice de l'article provenant de la source Cambridge University Press

For Kn = Q(ω) a real algebraic number field of degree n over Q such that with D ∊ N, d ∊ Z, d|D 2, and D 2 + 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 . 
Levesque, Claude. An Independent System of Units in Certain Algebraic Number Fields. Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 644-663. doi: 10.4153/CJM-1985-034-x
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[1] 1. Bernstein, L., Periodical continued fractions of degree n by Jacobi's algorithm, J. reine angew. Math. 213 (1964), 31–38. Google Scholar

[2] 2. Bernstein, L., Representation of as a periodic continued fraction by JacobVs algorithm, Math. Nachr. 29 (1965), 179–200. Google Scholar

[3] 3. Bernstein, L., Gaining units from units, Can. J. Math. 29 (1977), 93–106. Google Scholar

[4] 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), 160–163. Google Scholar

[5] 5. 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

[6] 6. Halter-Koch, F. und Stender, H.-J., Unabhangige Einheiten für die Körper , Abh. Math. Sem. Univ. Hamburg 42 (1974), 33–40. Google Scholar | DOI

[7] 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), 24–62. Google Scholar

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