Approximation par des nombres algébriques

Journal of Number Theory

Volumn 84, Issue 1, 2000, Pages 15-33

  Bugeaud, Yann ^a  

^a UNIVERSITÉ DE STRASBOURG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034258730     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jnth.2000.2517     Document Type: Article

References (22)

1. Baker A. Linear forms in the logarithms of algebraic numbers I, II, III, IV. Mathematika. 13:1966;204-216.
2. Bombieri E. On the Thue-Siegel-Dyson theorem. Acta Math. 148:1982;255-296.
3. Bombieri E., Mueller J. On effective measures of irrationality for a/b and related numbers. J. Reine Angew. Math. 342:1983;173-196.
4. Bombieri E., Mueller J. Remarks on the approximation to an algebraic number by algebraic numbers. Mich. Math. J. 33:1986;83-93.
5. Bugeaud Y., Györy K. Bounds for the solutions of Thue-Mahler equations and norm form equations. Acta Arith. 74:1996;273-292.
6. Diaz G. Une nouvelle propriété d'approximation diophantienne. C. R. Acad. Sci. Paris. 324:1997;969-972.
7. Feldman N. I. An effective refinement of the exponent in Liouville's theorem (en russe). Izv. Akad. Nauk. 35:1971;973-990.
8. Laurent M., Roy D. Criteria of algebraic independence with multiplicities and interpolation determinants. Trans. Amer. Math. Soc. 351:1999;1845-1870.
9. Laurent M., Roy D. Sur l'approximation algébrique en degré de transcendance un. Ann. Instit. Fourier. 49:1999;27-55.
10. Laurent M., Roy D. Criteria of algebraic independence with multiplicities and approximation by hypersurfaces. rapport CICMA. 1998.
11. Philippon P. Une approche méthodique pour la transcendance et l'indépendance algébrique de valeurs de fonctions analytiques. J. Number Theory. 64:1997;291-338.
12. Roth K. F. Rational approximations to algebraic numbers. Mathematika. 2:1955;1-20.
13. Roy D., Waldschmidt M. Quadratic relations between logarithms of algebraic numbers. Proc. Japan Acad. Ser. A. 71:1995;151-153.
14. Roy D., Waldschmidt M. Approximation diophantienne et indépendance algébrique de logarithmes. Ann. Sci. Ecole Norm. Sup. 30:1997;753-796.
15. Roy D., Waldschmidt M. Simultaneous approximation and algebraic independence. Ramanujan Math. J. 1:1997;379-430.
16. Schmidt W. M. Approximation to algebraic numbers. Monogr. Enseignement Math. 19:1971.
17. Schmidt W. M. Diophantine Approximation. Lecture Notes in Math. 785:1980;Springer-Verlag, Berlin.
18. Schneider T. Introduction aux nombres transcendants. 1959;Gauthier-Villars, Paris.
19. Sprindžuk V. G. Mahler's problem in metric number theory. Amer. Math. Soc. Trans. Math. Monogr. 25:1969.
20. M. Waldschmidt, Conjectures for Large Transcendence Degree, in, Number Theory Conference Graz, de Gruyter, Berlin.
21. Walters P. Ergodic Theory - Introductory Lectures. Lecture Notes in Math. 458:1975;Springer-Verlag, Berlin.
22. Wirsing E. Approximation mit algebraischen Zahlen beschränkten Grades. J. Reine Angew. Math. 206:1961;67-77.