  Let $K$ be a number field, and let $K(x_1,...,x_d)$ be the field of rational
fractions in the variables $x_1,...,x_d$. In this paper, we introduce two kinds
of Laplace transform adapted to solutions of the differential
$K(x_1,...,x_d)$-modules with regular singularities, and give some of their
basic differential and arithmetic properties. The purpose of this article is to
provide some tools which might be useful, in particular, for the arithmetic
study of the differential $K(x_1,...,x_d)$-modules associated to $E$-functions
in several variables.

Number Theory