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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A convergence problem connected with continued fractions


Author: Gerhard Larcher
Journal: Proc. Amer. Math. Soc. 103 (1988), 718-722
MSC: Primary 11J70
MathSciNet review: 947645
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Abstract | References | Similar Articles | Additional Information

Abstract: The set $ {Z_\alpha }: = \{ \beta \vert{\lim _{n \to \infty }}\vert\vert{q_n}\beta \vert\vert = 0\} $ is considered, where $ {\left( {{q_n}} \right)_{n \in {\mathbf{N}}}}$ is the sequence of best approximation denominators of $ \alpha $, and it is explicitly determined for $ \alpha $ with bounded continued fraction coefficients.


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

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  • [3] C. Mauduit, Uniform distribution of $ \alpha $-scale automata-sequences, Marseille, 1986 (to appear).
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0947645-2
PII: S 0002-9939(1988)0947645-2
Keywords: Continued fractions
Article copyright: © Copyright 1988 American Mathematical Society