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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: 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?)

  • [1] A. J. Brentjes, Multi-dimensional continued fraction algorithms, Mathematisch Centrum, Amsterdam, 1981. MR 638474 (83b:10038)
  • [2] L. Kuipers, and H. Niederreiter, Uniform distribution of sequences, Wiley, New York, 1974. MR 0419394 (54:7415)
  • [3] C. Mauduit, Uniform distribution of $ \alpha $-scale automata-sequences, Marseille, 1986 (to appear).
  • [4] O. Perron, Die Lehre von den Kettenbrüchen, Teubner, Stuttgart, 1954. MR 0064172 (16:239e)

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Keywords: Continued fractions
Article copyright: © Copyright 1988 American Mathematical Society

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