On the smallest poles of topological zeta functions
Abstract
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.
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