Continued fractions with circular twin value sets
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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.References
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Additional Information
- Lisa Lorentzen
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
- MR Author ID: 306381
- Received by editor(s): December 4, 2005
- Received by editor(s) in revised form: August 16, 2006
- Published electronically: March 12, 2008
- © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 4287-4304
- MSC (2000): Primary 40A15
- DOI: https://doi.org/10.1090/S0002-9947-08-04475-9
- MathSciNet review: 2395173