Existence of oblique polar lines for the meromorphic extension of the current valued function $int |f|^{2lambda}|g|^{2mu}square$ is given under the following hypotheses: $f$ and $g$ are holomorphic function germs in $CC^{n+1}$ such that $g$ is non-si
ngular, the germ $S:=ens{d fwedge d g =0}$ is one dimensional, and $g|_S$ is proper and finite. The main tools we use are interaction of strata for $f$ (see cite{B:91}), monodromy of the local system $H^{n-1}(u)$ on $S$ for a given eigenvalue $exp(-2ipi u)$ of the monodromy of $f$, and the monodromy of the cover $g|_S$. Two non-trivial examples are completely worked out.
We prove the following two results 1. For a proper holomorphic function $ f : X to D$ of a complex manifold $X$ on a disc such that ${df = 0 } subset f^{-1}(0)$, we construct, in a functorial way, for each integer $p$, a geometric (a,b)-module $E
^p$ associated to the (filtered) Gauss-Manin connexion of $f$. This first theorem is an existence/finiteness result which shows that geometric (a,b)-modules may be used in global situations. 2. For any regular (a,b)-module $E$ we give an integer $N(E)$, explicitely given from simple invariants of $E$, such that the isomorphism class of $Ebig/b^{N(E)}.E$ determines the isomorphism class of $E$. This second result allows to cut asymptotic expansions (in powers of $b$) of elements of $E$ without loosing any information.
