no. 1
Conjecture de Littlewood et récurrences linéaires
Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 249-266.

Ce travail est essentiellement consacré à la construction d’exemples effectifs de couples (α,β) de nombres réels à constantes de Markov finies, tels que 1,α et β soient 𝐙-linéairement indépendants, et satisfaisant à la conjecture de Littlewood.

This work is essentially devoted to construct effective examples of pairs of continued fractions (α,β) with bounded quotients, such that 1,α and β are 𝐙-linearly independent, and satisfying Littlewood’s conjecture.

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     author = {de Mathan, Bernard},
     title = {Conjecture de {Littlewood} et r\'ecurrences lin\'eaires},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {249--266},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     mrnumber = {2019015},
     zbl = {1045.11048},
     language = {fr},
     url = {http://www.numdam.org/item/JTNB_2003__15_1_249_0/}
}
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de Mathan, Bernard. Conjecture de Littlewood et récurrences linéaires. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 249-266. http://www.numdam.org/item/JTNB_2003__15_1_249_0/

[1] J.-P. Allouche, J.L. Davison, M. Queffélec, L.Q. Zamboni, Transcendence of Sturmian or morphic continued fractions, J. Number Theory 91 (2001), 39-66. | MR | Zbl

[2] J.W.S. Cassels, H.P.F. Swinnerton-Dyer, On the product of three homogeneous linear forms and indefinite ternary quadratic forms. Philos. Trans. Roy. Soc. London, Ser. A, 248 (1955), 73-96. | MR | Zbl

[3] L.G. Peck, Simultaneous rational approximations to algebraic numbers. Bull. Amer. Math. Soc. 67 (1961), 197-201. | MR | Zbl

[4] A.D. Pollington, S.L. Velani, On a problem in simultaneous Diophantine approximation: Littlewood's conjecture. Acta Math. 185 (2000), 287-306. | MR | Zbl

[5] M. Queffélec, Trcanscendance des fractions continues de Thue-Morse. J. Number Theory 73 (1998), 201-211. | MR | Zbl

[6] W.M. Schmidt, On simultaneous approximations of two algebraic numbers by rationals. Acta Math. 119 (1967), 27-50. | MR | Zbl

[7] W.M. Schmidt, Approximation to algebraic numbers. Enseignement math. 17 (1971), 187-253. | MR | Zbl