Adamczewski, Boris; Bugeaud, Yann On the decimal expansion of algebraic numbers. (English) Zbl 1138.11028 Fiz. Mat. Fak. Moksl. Semin. Darb. 8, 5-13 (2005). 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 \({\mathbf a}\). Reviewer: Clemens Heuberger (Graz) Cited in 3 Documents 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. Keywords:\(b\)-adic expansion; integer base; Fibonacci word; transcendence; normal number; Sturmian sequence PDFBibTeX XMLCite \textit{B. Adamczewski} and \textit{Y. Bugeaud}, Fiz. Mat. Fak. Moksl. Semin. Darb. 8, 5--13 (2005; Zbl 1138.11028)