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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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