  We associate to a filtered $\varphi$-module $D$ a sub-$Z_p[[x]]$-module of
convergent series on the open unit disk in which the $p$-adic $L$-functions of
the Galois representation associated to $D$ and the $Z_p$-cyclotomic extension
live (if they exist). This generalizes the already known case where $D$ is
associated to an elliptic curve or a modular form.

Number Theory