On the smallest poles of topological zeta functions

الأصل · EN

We study the local topological zeta function associated to a complex function that is holomorphic at the origin of C² (respectively C³). We determine all possible poles less than -1/2 (respectively -1). On C² our result is a generalization of the fact that the log canonical threshold is never in]5/6,1[. Similar statements are true for the motivic zeta function.