Monodromy eigenvalues and poles of zeta functions

The monodromy conjecture predicts that the poles of the topological zeta function and related zeta functions associated to a polynomial f induce monodromy eigenvalues of f. However, not every monodromy eigenvalue can be recovered from a pole. More generally, one also considers zeta functions associated to a polynomial and a differential form. We attach to f a suitable class of differential forms, such that each pole of the topological zeta function of f and such a form induces a monodromy eigenvalue, and moreover such that all monodromy eigenvalues are obtained this way.