Linear independence of continued fractions
Journal de Théorie des Nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 489-495.

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.

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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] P. Bundschuh, Transcendental continued fractions. J. Number Theory 18 (1984), 91-98. | MR 734440 | Zbl 0531.10035

[2] H. Davenport, K.F. Roth, Rational approximations to algebraic numbers. Mathematika 2 (1955), 160-167. | MR 77577 | Zbl 0066.29302

[3] G.M. Fichtengolc, Lecture on Differential and lntegrational Calculus II (Russian). Fizmatgiz, 1963.

[4] J. Hancl, Linearly unrelated sequences. Pacific J. Math. 190 (1999), 299-310. | MR 1722896 | Zbl 1005.11033

[5] J. Hancl, Continued fractional algebraic independence of sequences. Publ. Math. Debrecen 46 (1995), 27-31. | MR 1316646 | Zbl 0862.11045

[6] G.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers. Oxford Univ. Press, 1985. | MR 568909

[7] H.P. Schlickewei, A.J. Van Der Poorten, The growth conditions for recurrence sequences. Macquarie University Math. Rep. 82-0041, North Ryde, Australia, 1982.