Good approximations and continued fractions
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- by Cor Kraaikamp and Pierre Liardet PDF
- Proc. Amer. Math. Soc. 112 (1991), 303-309 Request permission
Abstract:
Let ${({q_n})_n}$ be the sequence of best approximation denominators of an irrational number $\alpha$. The set of real numbers $x$ for which ${q_n}x \to 0$ $(\bmod 1)$ is studied. It is shown that a number $x$ belongs to $\alpha \mathbb {Z}(\bmod {\text {1)}}$ if and only if a simple condition on the speed of the convergence related to an arithmetic property of $\alpha$ is satisfied. This set is uncountable whenever $\alpha$ has unbounded partial quotients.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 303-309
- MSC: Primary 11J70; Secondary 11J71
- DOI: https://doi.org/10.1090/S0002-9939-1991-1062392-7
- MathSciNet review: 1062392