## Euler-Poincaré characteristics, local zeta functions and analytic modifications. (Caractéristiques d’Euler-Poincaré, fonctions zêta locales et modifications analytiques.)(French)Zbl 0777.32017

For a complex analytic function $$f$$ new invariants are introduced, the topological zeta function. They are defined using the resolution of $$f$$ and using arithmetic results concerning the zeta function of Igusa. If $$f$$ is nondegenerated with respect to the Newton boundary then the zeta function can be computed in terms of the Newton boundary.
Reviewer: G.Pfister (Berlin)

### MSC:

 32S25 Complex surface and hypersurface singularities 32S45 Modifications; resolution of singularities (complex-analytic aspects) 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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