no. 5
On the rational approximation to the Thue–Morse–Mahler numbers
[Sur l’approximation rationnelle des nombres de Thue–Morse–Mahler]
Bugeaud, Yann1
1 Université de Strasbourg Département de Mathématiques 7, rue René Descartes 67084 STRASBOURG (France)
Annales de l'Institut Fourier, Tome 61 (2011) no. 5, pp. 2065-2076.

Soit (t k ) k≥0 la suite de Thue–Morse définie sur {0,1} par t 0 =0, t 2k =t k et t 2k+1 =1-t k pour k≥0. Soit b≥2 un entier rationnel. Nous démontrons que l’exposant d’irrationalité du nombre de Thue–Morse–Mahler ∑ k≥0 t k b -k est égal à 2.

Let (t k ) k≥0 be the Thue–Morse sequence on {0,1} defined by t 0 =0, t 2k =t k and t 2k+1 =1-t k for k≥0. Let b≥2 be an integer. We establish that the irrationality exponent of the Thue–Morse–Mahler number ∑ k≥0 t k b -k is equal to 2.

DOI : 10.5802/aif.2666
Classification : 11J04, 11J82
Keywords: Irrationality measure, Thue–Morse sequence, Padé approximant
Mot clés : mesure d’irrationalité, suite de Thue–Morse, approximant de Padé

Bugeaud, Yann 1

1 Université de Strasbourg Département de Mathématiques 7, rue René Descartes 67084 STRASBOURG (France) 
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Bugeaud, Yann. On the rational approximation to the Thue–Morse–Mahler numbers. Annales de l'Institut Fourier, Tome 61 (2011) no. 5, pp. 2065-2076. doi : 10.5802/aif.2666. https://aif.centre-mersenne.org/articles/10.5802/aif.2666/

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