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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, Multidimensional continued fraction algorithms, Mathematical Centre Tracts, vol. 145, Mathematisch Centrum, Amsterdam, 1981. MR 638474
  • [2] L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. MR 0419394
  • [3] C. Mauduit, Uniform distribution of $ \alpha $-scale automata-sequences, Marseille, 1986 (to appear).
  • [4] Oskar Perron, Die Lehre von den Kettenbrüchen. Bd I. Elementare Kettenbrüche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1954 (German). 3te Aufl. MR 0064172

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

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