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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Continued fractions and equivalent complex numbers


Author: Richard B. Lakein
Journal: Proc. Amer. Math. Soc. 42 (1974), 641-642
MSC: Primary 10F20
MathSciNet review: 0382179
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Abstract: In this note it is shown, by a counterexample, that the familiar theorem on the continued fraction expansions of equivalent numbers does not hold when these notions are extended to complex numbers.


References [Enhancements On Off] (What's this?)

  • [1] A. Hurwitz, Über die Entwicklung complexer Grössen in Kettenbrüche, Acta Math. 11 (1887), no. 1-4, 187–200 (German). MR 1554754, 10.1007/BF02418048
  • [2] A. Hurwitz, Über eine besondere Art der Kettenbruch-Entwicklung reeller Grössen, Acta Math. 12 (1889), no. 1, 367–405 (German). MR 1554778, 10.1007/BF02391885
  • [3] Julius Hurwitz, Über die Reduction der Binären Quadratischen Formen mit Complexen Coefficienten und Variabeln, Acta Math. 25 (1902), no. 1, 231–290 (German). MR 1554944, 10.1007/BF02419027
  • [4] A. Stein, Die Gewinnung der Einheiten in gewissen relativ-quadratischen Zahlkörpern durch das J. Hurwitzsche Kettenbruchverfahren, J. Reine Angew. Math. 156 (1927), 69-92.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0382179-8
Keywords: Complex continued fractions, equivalent complex numbers
Article copyright: © Copyright 1974 American Mathematical Society