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On the smallest poles of topological zeta functions

Dirk Segers·Willem Veys
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Abstract

We study the local topological zeta function associated to a complex function that is holomorphic at the origin of C^2 (respectively C^3). We determine all possible poles less than -1/2 (respectively -1). On C^2 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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Dirk Segers, Willem Veys. 2003-05-16. On the smallest poles of topological zeta functions. https://arxiv.org/abs/math/0305235

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