Equations différentielles $p$-adiques et Séries Gevrey arithmétiques

Abstract

Let $K$ be a number field. This paper is devoted to a $p$-adic study of the algebraic differential equation of $K[x,d/dx]$ with minimal degree in $x$ annihilating a given $E$-function. Precisely, we prove a conjecture of yves André (conjecture 4.7 of math.NT/0003238)

28 pages, French, version to appear in Math. Ann