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Abschätzung der Periodenlänge einer verallgemeinerten Kettenbruchentwicklung. (Estimate of the period length of a generalized continued fraction expansion). (German) Zbl 0567.10005
The author has found a periodic algorithm which corresponds for quadratic (resp. cubic) fields to the continued fraction (resp. Voronoi) algorithm. In the paper under review, he gives an upper bound for the length of the period of his algorithm in the case of a number field of degree n over \({\mathbb{Q}}\) whose unit rank is one: the length is O(\(\sqrt{D} \log^{n-1} D)\), where D is the absolute value of the discriminant of K, and the O- constant is explicitly given.
Reviewer: C.Levesque

11A55 Continued fractions
11J70 Continued fractions and generalizations
11R21 Other number fields
11A63 Radix representation; digital problems
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