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APPROXIMATING NUMBERS WITH MISSING DIGITS BY ALGEBRAIC NUMBERS
Published online by Cambridge University Press: 25 January 2007
Abstract
We show that for a given base $b$ and a proper subset $E\subset\{0,\dots,b-1\}$, $\#E\ltb-1$, the set of numbers $x\in[0,1]$ that have no digits from $E$ in their expansion to base $b$ consists almost exclusively of $S^*$-numbers of type at most $\min\{2,\log b/\log(b-\#E)\}$. We also give upper bounds on the Hausdorff dimension of some exceptional sets.
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 3 , October 2006 , pp. 657 - 666
- Copyright
- Copyright © Edinburgh Mathematical Society 2006
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