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Fundamental units and cycles. I. (English) Zbl 0352.10002

Cet ouvrage est une version détaillé d’un autre ouvrage [Pac. J. Math. 63, 37–61 (1976; Zbl 0335.10010)]. Le but principal est de donner une déscription explicite du dévelopement en fraction continue pour certaines classes de racines quadratiques.

MSC:

11A55 Continued fractions
11R11 Quadratic extensions
11R27 Units and factorization

Citations:

Zbl 0335.10010
Full Text: DOI

References:

[1] Bernstein, L., The Jacobi-Perron Algorithm, Its Theory and Application, (Lecture Notes in Mathmeatics Np. 207 (1971), Springer-Verlag: Springer-Verlag New York/Berlin), 1-160 · Zbl 0213.05201
[2] L. BernsteinAmer. Math. Monthly; L. BernsteinAmer. Math. Monthly
[3] Degert, G., Über die Bestimmung der Grundeinheit gewisser rell-quadratischer Zahlkörper, Hamburger Math. Abh., 22, 92-97 (1958) · Zbl 0079.05803
[4] Muir, Th, The expression of a quadratic surd as a continued fraction, Glasgow Math. J. (1874)
[5] Muir, Th, A new special class of determinants, (Proc. Edinburgh Math. Soc., 8 (1874)) · JFM 41.0187.04
[6] O. Perron,Chelsea,; O. Perron,Chelsea,
[7] Yamamoto, Y., Real quadratic number fields with large fundamental units, Osaka J. Math., 8, 261-271 (1971) · Zbl 0243.12001
[8] Zassenhaus, H., Units of orders, J. Algebra, 20, 368-395 (1972) · Zbl 0227.16006
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