Let be the Thue–Morse sequence on defined by , and for . Let be an integer. We establish that the irrationality exponent of the Thue–Morse–Mahler number is equal to .
Soit la suite de Thue–Morse définie sur par , et pour . Soit un entier rationnel. Nous démontrons que l’exposant d’irrationalité du nombre de Thue–Morse–Mahler est égal à .
Keywords: Irrationality measure, Thue–Morse sequence, Padé approximant
Mot clés : mesure d’irrationalité, suite de Thue–Morse, approximant de Padé
@article{AIF_2011__61_5_2065_0, author = {Bugeaud, Yann}, title = {On the rational approximation to the {Thue{\textendash}Morse{\textendash}Mahler} numbers}, journal = {Annales de l'Institut Fourier}, pages = {2065--2076}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {5}, year = {2011}, doi = {10.5802/aif.2666}, zbl = {1271.11074}, mrnumber = {2961848}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2666/} }
TY - JOUR AU - Bugeaud, Yann TI - On the rational approximation to the Thue–Morse–Mahler numbers JO - Annales de l'Institut Fourier PY - 2011 SP - 2065 EP - 2076 VL - 61 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2666/ DO - 10.5802/aif.2666 LA - en ID - AIF_2011__61_5_2065_0 ER -
%0 Journal Article %A Bugeaud, Yann %T On the rational approximation to the Thue–Morse–Mahler numbers %J Annales de l'Institut Fourier %D 2011 %P 2065-2076 %V 61 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2666/ %R 10.5802/aif.2666 %G en %F AIF_2011__61_5_2065_0
Bugeaud, Yann. On the rational approximation to the Thue–Morse–Mahler numbers. Annales de l'Institut Fourier, Volume 61 (2011) no. 5, pp. 2065-2076. doi : 10.5802/aif.2666. http://www.numdam.org/articles/10.5802/aif.2666/
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