Approximations diophantiennes des nombres sturmiens

Journal de Theorie des Nombres de Bordeaux

Volumn 14, Issue 2, 2002, Pages 613-628

  Queffélec, Martine ^a  

^a UNIVERSITÉ LILLE 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85009844438     PISSN: 12467405     EISSN: None     Source Type: Journal    
DOI: 10.5802/jtnb.378     Document Type: Article

References (28)

1. W. W. ADAMS, J. L. DAVISON, A remarkable class of continued fractions. Proc. Amer. Math. Soc. 65 (1977), 194-198.
2. 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.
3. J.-P. ALLOUCHE, L. Q. ZAMBONI, Algebraic irrational binary numbers cannot be fixed points of non-trivial constant length or primitive morphisms. J. Number Theory 69 (1998), 119-124.
4. P. ARNOUX, G. RAUZY, Représentation géométrique de suites de complexité 2n + 1. Bull. Soc. Math. France 119 (1991), 199-215.
5. V. BERTHÉ, Fréquences des facteurs des suites sturmiennes. Theoret. Comput. Sci. 165 (1996), 295-309.
6. P. E. BÖHMER, Über die Transzendenz gewisser dyadischer Brüche. Math. Ann. 96 (1926), 367-377. Erratum ibid. page 735.
7. T. BOUSCH, Le poisson n’a pas d’arête. Ann. Inst. H. Poincaré Probab. Stat. 36 (2000) 489-508.
8. S. BULLETT, P. SENTENAC, Ordered orbits of the shift, square roots, and the devil’s staircase. Math. Proc. Camb. Philos. Soc. 115 (1994), 451-481.
9. L.V. DANILOV, Some classes of transcendent al numbers. English Translation in Math. Notes Acad. Sci. USSR 12 (1972), 524-527.
10. J. L. DAVISON, A series and its associated continued fraction. Proc. Amer. Math. Soc. 63 (1977), 29-32.
11. F. M. DEKKING, Transcendance du nombre de Thue-Morse. C. R. Acad. Sci. Paris, Sér. A-B 285 (1977), 157-160.
12. F. M. DEKKING, On the Thue-Morse measure. Acta Universitatis Carolinae, Math. Phys. 33 (1992), 35-40.
13. S. FERENCZI, C. MAUDUIT, Transcendence of numbers with a low complexity expansion. J. Number Theory 67 (1997), 146-161.
14. G. H. HARDY, E. M. WRIGHT, An introduction to the theory of numbers. Clarendon Press, Oxford Univ. Press, 1979.
15. A. HURWITZ, Über die Kettenbruch-Entwicklung der Zahl e. Mathematische Werke, Bd 2 Basel, Birkhaüser, 1933, 129-133.
16. T. KOMATSU, A certain power series and the inhomogeneous continued fraction expansions. J. Number Theory 59 (1996), 291-312.
17. P. LIARDET, P. STAMBUL, Séries de Engel et fractions continuées. J. Théor. Nombres Bordeaux 12 (2000), 37-68.
18. J. H. LOXTON, A. J. VAN DER POORTEN, Arithmetic properties of the solutions of a class of functional equations. J. Reine Angew. Math. 330 (1982), 159-172.
19. M. MORSE, G. A. HEDLUND, Symbolic dynamics II : Sturmian trajectories. Amer. J. Math. 62 (1940), 1-42.
20. K. NISHIOKA, I. SHIOKAWA, J.-I. TAMURA, Arithmetical properties of a certain power series. J. Number Theory 42 (1992), 61-87.
21. G. N. RANEY, On continued fractions and finite automata. Math. Ann. 206 (1973), 265-283.
22. D. RIDOUT, Rational approximations to algebraic numbers. Mathematika 4 (1957), 125-131.
23. K. F. ROTH, Rational approximations to algebraic numbers. Mathematika 2 (1955), 1-20. Corrigendum, page 168.
24. R. N. RISLEY, L. Q. ZAMBONI, A generalization of Sturmian sequences: combinatorial structure and transcendence. Acta Arith. 95 (2000) 167-184.
25. J. SHALLIT, Real numbers with bounded partial quotients: a survey. Enseign. Math. 38 (1992), 151-187.
26. H. J. S. SMITH, Note on continued fractions. Messenger Math. 6 (1876), 1-14.
27. J.-I. TAMURA, A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension. Acta Arith. 71 (1995), 301-329.
28. A. J. VAN DER POORTEN, An introduction to continued fractions. In Diophantine Analysis London Math. Soc. Lecture Note Ser., 109, Cambridge University Press, 1986, 99-138.