Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1974-0382179-8
MathSciNet review: 0382179
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 komplexer Grössen in Kettenbrüche, Acta Math. 11 (1888), 187-200 (= Werke II, 72-83). MR 1554754
  • [2] -, Über eine besondere Art der Kettenbruch-Entwicklung reeller Grössen, Acta Math. 12 (1889), 367-405. (= Werke II, 84-115). MR 1554778
  • [3] J. Hurwitz, Über die Reduction der binären quadratischen Formen mit complexen Coefficienten und Variabeln, Acta Math. 25 (1902), 231-290. MR 1554944
  • [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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10F20

Retrieve articles in all journals with MSC: 10F20


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

American Mathematical Society