Burger, Edward B.; van der Poorten, Alfred J. 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]. Reviewer: Richard A.Mollin (Calgary) Cited in 2 Documents MSC: 11J70 Continued fractions and generalizations 11R27 Units and factorization 11J13 Simultaneous homogeneous approximation, linear forms 11R11 Quadratic extensions Keywords:purely periodic continued fraction expansions; quadratic irrationals; quadratic field; group of units Citations:Zbl 0971.11039 PDFBibTeX XMLCite \textit{E. B. Burger} and \textit{A. J. van der Poorten}, CMS Conf. Proc. 27, 35--43 (2000; Zbl 0971.11040)