Approximation diophantienne et approximants de Hermite-Padé de type I de fonctions exponentielles

Details Approximation diophantienne et approximants de Hermite-Padé de type I de fonctions exponentielles Approximation diophantienne et approximants de Hermite-Padé de type I de fonctions exponentielles

2010-01-11

arxiv.org/abs/1001.1766v1

Ann. Sci. Math. Qu\'ebec 35 (2011), no 1, 85-116

Mathematics

Number Theory

accepted in Annales des sciences math\'ematiques du Qu\'ebec (special issue dedicated to Paulo Ribenboim)

Scientific paper

En utilisant des approximants de Hermite-Pad\'e de fonctions exponentielles, ainsi que des d\'eterminants d'interpolation de Laurent, nous minorons la distance entre un nombre alg\'ebrique et l'exponentielle d'un nombre alg\'ebrique non nul. ----- We use Hermite-Pad\'e approximants of exponential functions along with Laurent's interpolation determinants to obtain lower bounds for the distance between an algebraic number and the exponential of another non-zero algebraic number.

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