On Maximal order poles of generalized topological zeta functions

We show some examples of topological zeta functions associated to an isolated plane curve singular point and an allowed, in the sense of Némethi and Veys, differential form that have several poles of order two. This is in contrast to the case of the standard differential form where, as showed by Veys for plane curves and by Nicaise and Xu in general, there is always at most one pole of order two.