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On the decimal expansion of algebraic numbers. (English) Zbl 1138.11028

Let \(0\leq \xi\leq 1\) be a real number and \({\mathbf a}=a_1a_2\ldots\) be its \(b\)-adic expansion, i.e., \(\xi=\sum_{j\geq 1}a_j b^{-j}\). In this expository paper, the authors give an overview on transcendence results based on the complexity \(p(n,\xi,b)\) of \(\xi\), i.e., the number of distinct blocks of length \(n\) occurring in \({\mathbf a}\).

MSC:

11J81 Transcendence (general theory)
11A63 Radix representation; digital problems
11B85 Automata sequences
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
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