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3 results

  • On the smallest poles of topological zeta functions

  • Dirk Segers, Willem Veys
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 1 / January 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 130-144
    Print publication:
    January 2004
    • Article
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  • 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.