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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A convergence problem connected with continued fractions
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by Gerhard Larcher
Proc. Amer. Math. Soc. 103 (1988), 718-722
DOI: https://doi.org/10.1090/S0002-9939-1988-0947645-2

Abstract:

The set ${Z_\alpha }: = \{ \beta |{\lim _{n \to \infty }}||{q_n}\beta || = 0\}$ 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
  • A. J. Brentjes, Multidimensional continued fraction algorithms, Mathematical Centre Tracts, vol. 145, Mathematisch Centrum, Amsterdam, 1981. MR 638474
  • L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0419394
  • C. Mauduit, Uniform distribution of $\alpha$-scale automata-sequences, Marseille, 1986 (to appear).
  • 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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Bibliographic Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 718-722
  • MSC: Primary 11J70
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0947645-2
  • MathSciNet review: 947645