Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T18:51:00.785Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximation algébrique simultanée de nombres de Liouville

Published online by Cambridge University Press:  20 November 2018

Damien Roy
Damien Roy*
Affiliation:
Département de Mathématiques et de Statistiques Université d’Ottawa Ottawa, Ontario K1N 6N5
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to show the limitations of the conjectures of algebraic approximation. For this, we construct points of ${{\mathbf{C}}^{m}}$ which do not admit good algebraic approximations of bounded degree and height, when the bounds on the degree and the height are taken from specific sequences. The coordinates of these points are Liouville numbers.

Keywords

11J82
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 1 , 01 March 2001 , pp. 115 - 120
Copyright
Copyright © Canadian Mathematical Society 2001

References

[1] Laurent, M., New methods in algebraic independence. In: Number Theory (eds. Györy, Pethö and Śos), Walter de Gruyter, Berlin, 1998, 311–330.Google Scholar
[2] Laurent, M. et Roy, D., Sur l’approximation algébrique en degré de transcendance un. Ann. Inst. Fourier 49(1999), à paraître.Google Scholar
[3] Philippon, P., Une approche méthodique pour la transcendance et l’indépendance algébrique de valeurs de fonctions analytiques. J.Number Theory 64 (1997), 291–338.Google Scholar
[4] Roy, D. and Waldschmidt, M., Simultaneous approximation and algebraic independence. The Ramanujan Journal 1 (1997), 379–430.Google Scholar