The Bulletin of the London Mathematical Society vol:42 issue:2 pages:312-322
The ‘monodromy conjecture’ for a hypersurface singularity f predicts that a pole of its topological (or related) zeta function induces one of its monodromy eigenvalues. However, in general only a few eigenvalues are obtained this way. The second author proposed to consider zeta functions associated with the hypersurface and with a differential form and raised the following question. Can one find a list of differential forms ωi such that any pole of the zeta function of f and an ωi induces a monodromy eigenvalue of f, and such that all monodromy eigenvalues of f are obtained this way? Here we provide an affirmative answer for an arbitrary irreducible curve singularity f.