Some New Applications of the Subspace Theorem

By Pietro Corvaja, Umberto Zannier. Compositio Mathematica, 2002

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On the complexity of algebraic numbers I. Expansions in integer bases (2005, background): “Note that Adamczewski [1] and Corvaja and Zannier [16] proved that, under a stronger assumption on the sequence (ak)k≥1, the number α defined in the statement of Theorem 5 is transcendental.”
Dynamics for β-shifts and Diophantine approximation (2007, methodology): “We say that a real number β > 1 is a self-lacunary number if there exist a positive real number δ and a sequence (un)n≥1 of positive integers satisfying the following lacunarity condition: u1 = 1 and un+1 un ≥ 1 + δ for n ≥ 1, (4.1) such that 1 = +∞∑ n=1 1 βun · (4.2) As a consequence of a nice resu”