Nous étudions les ensembles des valeurs prises par les exposants d’approximation quadratique et évalués aux nombres réels dont la suite des quotients partiels est engendrée par un automate fini. Entre autres résultats, nous montrons que ces ensembles contiennent tout nombre rationnel suffisamment grand et également des nombres transcendants.
We study the sets of values taken by the exponents of quadratic approximation and evaluated at real numbers whose sequence of partial quotients is generated by a finite automaton. Among other results, we show that these sets contain every sufficiently large rational number and also some transcendental numbers.
Mots-clés : Continued fraction, approximation by quadratic numbers, automatic sequence.
@article{JTNB_2015__27_2_463_0,
author = {Bugeaud, Yann},
title = {Quadratic approximation to automatic continued fractions},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {463--482},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {27},
number = {2},
year = {2015},
doi = {10.5802/jtnb.910},
mrnumber = {3393163},
zbl = {06504489},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.910/}
}
TY - JOUR AU - Bugeaud, Yann TI - Quadratic approximation to automatic continued fractions JO - Journal de théorie des nombres de Bordeaux PY - 2015 SP - 463 EP - 482 VL - 27 IS - 2 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.910/ DO - 10.5802/jtnb.910 LA - en ID - JTNB_2015__27_2_463_0 ER -
%0 Journal Article %A Bugeaud, Yann %T Quadratic approximation to automatic continued fractions %J Journal de théorie des nombres de Bordeaux %D 2015 %P 463-482 %V 27 %N 2 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.910/ %R 10.5802/jtnb.910 %G en %F JTNB_2015__27_2_463_0
Bugeaud, Yann. Quadratic approximation to automatic continued fractions. Journal de théorie des nombres de Bordeaux, Tome 27 (2015) no. 2, pp. 463-482. doi : 10.5802/jtnb.910. http://www.numdam.org/articles/10.5802/jtnb.910/
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