Equations différentielles $p$-adiques et Séries Gevrey arithmétiques

Details Equations différentielles $p$-adiques et Séries Gevrey arithmétiques Equations différentielles $p$-adiques et Séries Gevrey arithmétiques

2005-11-12

arxiv.org/abs/math/0511317v1

Mathematics

Number Theory

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

Scientific paper

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)

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