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Minorations de Combinaisons Linéaires de Logarithmes de Nombres Algébriques

Published online by Cambridge University Press:  20 November 2018

Michel Waldschmidt
Michel Waldschmidt*
Affiliation:
Université P. et M. Curie (Paris VI),C.N.R.S. “Problèmes Diophantiens“, Institut Henri Poincaré, II, rue P. et M. Curie, 75231 Paris Cedex 05
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On sait que la méthode classique de Schneider (en une variable) permet de minorer des combinaisons linéaires de deux logarithmes de nombres algébriques avec des coefficients algébriques. Nous généralisons cette méthode en plusieurs variables pour minorer des combinaisons linéaires de plusieurs logarithmes.

Abstract

Abstract

It's well known that Schneider's classical method (involving functions of a single complex variable) yields lower bounds for linear combinations of two logarithms of algebraic numbers with algebraic coefficients. We extend this method to functions of several variables and deduce an estimate for linear combinations of several logarithms.

Keywords

11 J 86
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 1 , 01 February 1993 , pp. 176 - 224
Copyright
Copyright © Canadian Mathematical Society 1993

References

Références

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