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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Continued fractions with circular twin value sets


Author: Lisa Lorentzen
Journal: Trans. Amer. Math. Soc. 360 (2008), 4287-4304
MSC (2000): Primary 40A15
Published electronically: March 12, 2008
MathSciNet review: 2395173
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Abstract: We prove that if the continued fraction $ K(a_{n}/1)$ has circular twin value sets $ \langle V_{0},V_{1}\rangle $, then $ K(a_{n}/1)$ converges except in some very special cases. The results generalize previous work by Jones and Thron.


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Additional Information

Lisa Lorentzen
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04475-9
PII: S 0002-9947(08)04475-9
Received by editor(s): December 4, 2005
Received by editor(s) in revised form: August 16, 2006
Published electronically: March 12, 2008
Article copyright: © Copyright 2008 American Mathematical Society