Conjecture de Littlewood et récurrences linéaires

Bernard de Mathan

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 1, page 249-266
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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de Mathan, Bernard. "Conjecture de Littlewood et récurrences linéaires." Journal de théorie des nombres de Bordeaux 15.1 (2003): 249-266. <http://eudml.org/doc/249094>.

@article{deMathan2003,
abstract = {Ce travail est essentiellement consacré à la construction d’exemples effectifs de couples $(\alpha , \beta )$ de nombres réels à constantes de Markov finies, tels que $1, \alpha $ et $\beta $ soient $\mathbf \{Z\}$-linéairement indépendants, et satisfaisant à la conjecture de Littlewood.},
author = {de Mathan, Bernard},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {effective construction},
language = {fre},
number = {1},
pages = {249-266},
publisher = {Université Bordeaux I},
title = {Conjecture de Littlewood et récurrences linéaires},
url = {http://eudml.org/doc/249094},
volume = {15},
year = {2003},
}

TY - JOUR
AU - de Mathan, Bernard
TI - Conjecture de Littlewood et récurrences linéaires
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 249
EP - 266
AB - Ce travail est essentiellement consacré à la construction d’exemples effectifs de couples $(\alpha , \beta )$ de nombres réels à constantes de Markov finies, tels que $1, \alpha $ et $\beta $ soient $\mathbf {Z}$-linéairement indépendants, et satisfaisant à la conjecture de Littlewood.
LA - fre
KW - effective construction
UR - http://eudml.org/doc/249094
ER -

References

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  1. [1] J.-P. Allouche, J.L. Davison, M. Queffélec, L.Q. Zamboni, Transcendence of Sturmian or morphic continued fractions, J. Number Theory91 (2001), 39-66. Zbl0998.11036MR1869317
  2. [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. Zbl0065.27905MR70653
  3. [3] L.G. Peck, Simultaneous rational approximations to algebraic numbers. Bull. Amer. Math. Soc.67 (1961), 197-201. Zbl0098.26302MR122772
  4. [4] A.D. Pollington, S.L. Velani, On a problem in simultaneous Diophantine approximation: Littlewood's conjecture. Acta Math.185 (2000), 287-306. Zbl0970.11026MR1819996
  5. [5] M. Queffélec, Trcanscendance des fractions continues de Thue-Morse. J. Number Theory73 (1998), 201-211. Zbl0920.11045MR1658023
  6. [6] W.M. Schmidt, On simultaneous approximations of two algebraic numbers by rationals. Acta Math.119 (1967), 27-50. Zbl0173.04801MR223309
  7. [7] W.M. Schmidt, Approximation to algebraic numbers. Enseignement math.17 (1971), 187-253. Zbl0226.10033MR327672

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