Exponents of diophantine approximation and sturmian continued fractions

Annales de l'Institut Fourier

Volumn 55, Issue 3, 2005, Pages 773-804

  Bugeaud, Yann ^a   Laurent, Michel ^b  

^a UNIVERSITÉ DE STRASBOURG   (France)

^b AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

Diophantine approximation; Simultaneous approximation; Sturmian sequence; Transcendence measure

Indexed keywords

EID: 33746614765     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.2114     Document Type: Article

References (32)

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. (Pubitemid 33132700)
3. B. ARBOUR, D. ROY, A Gel'fond type criterion in degree two, Acta Arith., 11(2004), 97-103.
4. A. BAKER, W. M. SCHMIDT, Diophantine approximation and Hausdorff dimension, Proc. London Math. Soc., 21(1970), 1-11.
5. R. C. BAKER, On approximation with algebraic numbers of bounded degree, Mathematika, 23(1976), 18-31.
6. V. I. BERNIK, Application of the Hausdorff dimension in the theory of Diophantine approximations, Acta Arith., 42(1983), 219-253 (en Russe);
7. English transl. in Amer. Math. Soc. Transl. 140(1988), 15-44.
8. Y. BUGEAUD, On the approximation by algebraic numbers with bounded degree, Algebraic number theory and Diophantine analysis (Graz, 1998), p. 47-53, de Gruyter, Berlin, 2000.
9. Y. BUGEAUD, Approximation par des nombres algebriques, J. Number Theory, 84(2000), 15-33.
10. Y. BUGEAUD, Mahler's classification of numbers compared with Koksma's, Acta Arith., 110(2003), 89-105. (Pubitemid 37052773)
11. Y. BUGEAUD, Approximation by algebraic numbers, Cambridge Tracts in Math., vol. 160, Cambridge University Press, 2004.
12. Y. BUGEAUD, O. TEULIÉ, Approximation d'un nombre réel par des nombres algébriques de degré donné, Acta Arith., 93(2000), 77-86.
13. J. CASSAIGNE, Limit values of the recurrence quotient of Sturmian sequences, Theor. Comput. Sci., 218(1999), 3-12. (Pubitemid 129609644)
14. H. DAVENPORT, W. M. SCHMIDT, Approximation to real numbers by quadratic irrationals, Acta Arith., 13(1967), 169-176.
15. H. DAVENPORT, W. M. SCHMIDT, Approximation to real numbers by algebraic integers, Acta Arith., 15(1969), 393-416.
16. H. DAVENPORT, W. M. SCHMIDT, Dirichlet's theorem on Diophantine approximation, Symposia Mathematica, vol. IV (INDAM, Rome, 1968/69), p. 113-132, Academic Press, London, 1970.
17. J. L. DAVISON, A series and its associated continued fraction, Proc. Amer. Math. Soc., 63(1977), 29-32.
18. K. FALCONER, The geometry of fractal sets, Cambridge Tracts in Mathematics, vol. 85, Cambridge University Press, 1985.
19. V. JARNÍK, Zur metrischen Theorie der diophantischen Approximationen, Prace Mat.-Fiz., 36(1928/29), 91-106.
20. V. JARNÍK, Zum Khintchineschen 'übertragungssatz', Trav. Inst. Math. Tbilissi, 3(1938), 193-212.
21. J. F. KOKSMA, Über die Mahlersche Klasseneinteilung der transzendenten Zahlen und die Approximation komplexer Zahlen durch algebraische Zahlen, Monats. Math. Phys., 48(1939), 176-189.
22. M. LAURENT, Some remarks on the approximation of complex numbers by algebraic numbers, Proceedings of the 2nd Panhellenic Conference in Algebra and Number Theory (Thessaloniki, 1998), Bull. Greek Math. Soc., 42(1999), 49-57.
23. M. LAURENT, Simultaneous rational approximation to the successive powers of a real number, Indag. Math., 11(2003), 45-53. (Pubitemid 37103567)
24. K. MAHLER, Zur Approximation der Exponentialfunktionen und des Logarithmus. I, II, J. reine angew. Math., 166(1932), 118-150.
25. M. QUEFFÉLEC, Approximations diophantiennes des nombres sturmiens, J. Théor. Nombres Bordeaux, 14(2002), 613-628.
26. A. M. ROCKETT, P. SZÜSZ, Continued Fractions, World Scientific, Singapore, 1992.
27. D. ROY, Approximation simultanee d'un nombre et son carré, C. R. Acad. Sci. Paris, 336(2003), 1-6. (Pubitemid 36656861)
28. D. ROY, Approximation to real numbers by cubic algebraic numbers, I, Proc. London Math. Soc., 88(2004), 42-62. (Pubitemid 38284643)
29. D. ROY, Approximation to real numbers by cubic algebraic numbers, II, Ann. of Math., 158(2003), 1081-1087. (Pubitemid 38285157)
30. D. ROY, Diophantine approximation in small degree, CRM Proceedings and Lecture Notes, vol. 36, p. 269-285, Amer. Math. Soc., 2004.
31. V. G. SPRINDŽUK, Mahler's problem in metric number theory, Amer. Math. Soc, Transl. Math. Monogr., vol. 25, Providence, R. I., 1969.
32. E. WIRSING, Approximation mit algebraischen Zahlen beschränkten Grades, J. reine angew. Math., 206(1961), 67-77.