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On periods of elements from real quadratic number fields. (English) Zbl 0971.11040

Théra, Michel (ed.), Constructive, experimental, and nonlinear analysis. Selected papers of a workshop, Limoges, France, September 22-23, 1999. Providence, RI: American Mathematical Society (AMS), publ. for the Canadian Mathematical Society. CMS Conf. Proc. 27, 35-43 (2000).
The authors look at criteria for two purely periodic continued fraction expansions to both represent quadratic irrationals in the same quadratic field, a phenomenon already reported and proved by the first author [in Monatsh. Math. 128, 201-209 (1999; Zbl 0971.11039)]. However, what they show in this paper is that the criteria are related to the group of units in the real quadratic field in a natural way. Their means of presenting the rather palatable results provide an engaging and lively read.
For the entire collection see [Zbl 0954.00025].

MSC:

11J70 Continued fractions and generalizations
11R27 Units and factorization
11J13 Simultaneous homogeneous approximation, linear forms
11R11 Quadratic extensions

Citations:

Zbl 0971.11039
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