Continued fractions with circular twin value sets

Lorentzen, Lisa

doi:10.1090/S0002-9947-08-04475-9

Continued fractions with circular twin value sets
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Trans. Amer. Math. Soc. 360 (2008), 4287-4304 Request permission

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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