Approximation diophantienne et approximants de Hermite-Pad\'e de type I de fonctions exponentielles

TL;DR

This paper develops new lower bounds on the distance between algebraic numbers and their exponentials using Hermite-Padé approximants and Laurent interpolation determinants, advancing Diophantine approximation theory.

Contribution

It introduces a novel method combining Hermite-Padé approximants and Laurent determinants to improve bounds in exponential Diophantine approximation.

Findings

Established new lower bounds for algebraic number and exponential differences

Applied Hermite-Padé approximants to exponential functions

Enhanced techniques in Diophantine approximation

Abstract

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.