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Article Dans Une Revue Mathematical Proceedings of the Cambridge Philosophical Society Année : 2009

Irrationality measures for some automatic real numbers

Boris Adamczewski
Tanguy Rivoal

Résumé

This paper is devoted to the rational approximation of automatic real numbers, that is, real numbers whose expansion in an integer base can be generated by a finite automaton. We derive upper bounds for the irrationality exponent of famous automatic real numbers associated with the Thue–Morse, Rudin–Shapiro, paperfolding and Baum–Sweet sequences. These upper bounds arise from the construction of some explicit Padé or Padé type approximants for the generating functions of these sequences. In particular, we prove that the Thue–Morse–Mahler numbers have an irrationality exponent at most equal to 4. We also obtain an explicit description of infinitely many convergents to these numbers.

Dates et versions

hal-02118290 , version 1 (02-05-2019)

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Boris Adamczewski, Tanguy Rivoal. Irrationality measures for some automatic real numbers. Mathematical Proceedings of the Cambridge Philosophical Society, 2009, 147 (3), pp.659-678. ⟨10.1017/S0305004109002643⟩. ⟨hal-02118290⟩
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