  For a simple complete ideal $\wp$ of a local ring at a closed point on a
smooth complex algebraic surface, we introduce an algebraic object, named
Poincar\'e series $P_{\wp}$, that gathers in an unified way the jumping numbers
and the dimensions of the vector space quotients given by consecutive
multiplier ideals attached to $\wp$. This paper is devoted to prove that
$P_{\wp}$ is a rational function giving an explicit expression for it.
