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://www.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://www.numdam.org/item/JTNB_2002__14_2_489_0/
[1] Transcendental continued fractions. J. Number Theory 18 (1984), 91-98. | MR | Zbl
,[2] Rational approximations to algebraic numbers. Mathematika 2 (1955), 160-167. | MR | Zbl
, ,[3] Lecture on Differential and lntegrational Calculus II (Russian). Fizmatgiz, 1963.
,[4] Linearly unrelated sequences. Pacific J. Math. 190 (1999), 299-310. | MR | Zbl
,[5] Continued fractional algebraic independence of sequences. Publ. Math. Debrecen 46 (1995), 27-31. | MR | Zbl
,[6] An Introduction to the Theory of Numbers. Oxford Univ. Press, 1985. | MR
, ,[7] The growth conditions for recurrence sequences. Macquarie University Math. Rep. 82-0041, North Ryde, Australia, 1982.
, ,