Automatic Sequences: Theory, Applications, Generalizations

By J. Allouche, J. Shallit. 2003

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On the complexity of algebraic numbers I. Expansions in integer bases (2005, methodology): “ence of Theorem 1, we give in Section 5 a short proof of it, that rests on another result of Cobham [14]. Theorem 2 establishes a particular case of the following widely believed conjecture (see e.g. [5]). The deﬁnitions of morphism, recurrent morphism, and morphic number are recalled in Section 3. ”
Diophantine approximation and Cantor sets (2008, background): “Remark 6 We refer the reader to [2] for the definitions of the notions discussed in this remark.”
Exponents of Diophantine approximation (2006, background): “atic, or transcendental, by (12). As noted in [1, 2], this observation gives a very short proof of the transcendence of the Thue–Morse continued fraction, ﬁrst established by Queﬀ´elec [41] (see also [4]). For any n≥ 2, denote by Qn the denominator of the rational number whose partial quotients are ”