A convergence problem connected with continued fractions
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- by Gerhard Larcher PDF
- Proc. Amer. Math. Soc. 103 (1988), 718-722 Request permission
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
Additional 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