no. 5
On the rational approximation to the Thue–Morse–Mahler numbers
[Sur l’approximation rationnelle des nombres de Thue–Morse–Mahler]
Bugeaud, Yann1
1Université 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

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.

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.

DOI : 10.5802/aif.2666
Classification : 11J04, 11J82
Keywords: Irrationality measure, Thue–Morse sequence, Padé approximant
Mots-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) 
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
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