Equations diff\'erentielles $p$-adiques et S\'eries Gevrey   arithm\'etiques
  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 Andr\'e (conjecture 4.7 of math.NT/0003238) 
Said Manjra, Salah-eddine Remmal