Nous donnons un critère d'indépendance linéaire sur le corps des rationnels qui s'applique à une famille donnée de nombres réels dont les développements en fractions continues satisfont certaines conditions.
The main result of this paper is a criterion for linear independence of continued fractions over the rational numbers. The proof is based on their special properties.
@article{JTNB_2002__14_2_489_0, author = {Han\v{c}l, Jaroslav}, title = {Linear independence of continued fractions}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {489--495}, publisher = {Universit\'e Bordeaux I}, volume = {14}, number = {2}, year = {2002}, mrnumber = {2040689}, zbl = {1067.11039}, language = {en}, url = {http://archive.numdam.org/item/JTNB_2002__14_2_489_0/} }
Hančl, Jaroslav. Linear independence of continued fractions. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 489-495. http://archive.numdam.org/item/JTNB_2002__14_2_489_0/
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