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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
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Full Text: DOI

References:

[1] Bernstein, L, The Jacobi-Perron algorithm, its theory and application, (), 1-160
[2] {\scL. Bernstein}, Periodicity and units in quadratic number fields, Amer. Math. Monthly, submitted.
[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, () · JFM 41.0187.04
[6] {\scO. Perron,} “Die Lehre von den Kettenbrüchen, Zweite verbesserte Auflage” I-XII, 1-542, Chelsea, New York.
[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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