Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T18:33:56.296Z Has data issue: false hasContentIssue false
  • English
  • Français

Independance algebrique des derivees d'une periode du module de Carlitz

Part of: Diophantine approximation, transcendental number theory Arithmetic algebraic geometry

Published online by Cambridge University Press:  09 April 2009

Laurent Denis
Laurent Denis
Affiliation:
Université des Sciences et Technologies de LilleUFR de Mathématiques 59655 Villeneuve d'AsqFrance e-mail: [email protected]
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.

We prove here that the p - 1 first derivatives of the fundamental period of the Carliz module are algebraically independent. For that purpose we will show to use Mahler's method in this situtaion.

MSC classification

Secondary: 11G09: Drinfel'd modules; higher-dimensional motives, etc. 11J85: Algebraic independence; Gel'fond's method
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 1 , August 2000 , pp. 8 - 18
Copyright
Copyright © Australian Mathematical Society 2000

References

[B1]Becker, P. G., ‘Algebraic independence of the values of vertain series by Mahler's method’, Monatsh. Math. 4 (1992), 183–198.CrossRefGoogle Scholar
[B2]Becker, P. G., ‘Transcendence measures for the values of generalized Mahler functions in arbitrary characteristic’, Pubn. Math. Debrecen 45 (1994), 269–282.CrossRefGoogle Scholar
[B]Brownawell, D., ‘Linear independence and divided derivatives of a Drinfeld module I’, in Proceedings of Schinzel Conference, Zakopane, Poland (Walter de Gruyter, Berlin, 1998) to appear.Google Scholar
[BD]Brownawell, D. and Denis, L., ‘Linear independence and hyperderivatives on Drinfeld modules II’, Proc. Amer. Math.. Soc., to appear.Google Scholar
[C]Carlitz, L., ‘On certain functions connected with polynomials in a Galois field’, Duke Math. J. 1 (1935), 137–168.CrossRefGoogle Scholar
[D1]Denis, L., ‘Dérivées d'un module de Drinfeld et transcendance’, Duke Math. J. 80 (1995), 1–13.CrossRefGoogle Scholar
[D2]Denis, L., ‘Indépendance algébrique en caractéristique deux’, J. Number Theory 66 (1997), 183–200.CrossRefGoogle Scholar
[D3]Denis, L., ‘Indépendance algébrique de différents π’, C. R. Acad. Sci. Paris 327 (1998), 711–714.CrossRefGoogle Scholar
[N]Nishioka, K., Mahler functions and transcendence, Lecture Notes in Math. 1631 (Springer, Berlin, 1987).Google Scholar
[P]Philippon, P., ‘cirtères pour I'indépendance algébrique dans les anneaux Diophantiens’, C. R.. Acad. Sci. Paris 315 (1992), 511–515.Google Scholar