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On the smallest poles of topological zeta functions
Published online by Cambridge University Press: 04 December 2007
Abstract
We study the local topological zeta function associated to a complex function that is holomorphic at the origin of $\mathbb{C}^2$ (respectively $\mathbb{C}^3$). We determine all possible poles less than −1/2 (respectively −1). On $\mathbb{C}^2$ 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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- Foundation Compositio Mathematica 2004
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