Monodromy eigenvalues and zeta functions with differential forms |
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Authors: | Willem Veys |
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Institution: | K.U.Leuven, Departement Wiskunde, Celestijnenlaan 200B, B-3001 Leuven, Belgium |
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Abstract: | For a complex polynomial or analytic function f, there is a strong correspondence between poles of the so-called local zeta functions or complex powers ∫|f|2sω, where the ω are C∞ differential forms with compact support, and eigenvalues of the local monodromy of f. In particular Barlet showed that each monodromy eigenvalue of f is of the form , where s0 is such a pole. We prove an analogous result for similar p-adic complex powers, called Igusa (local) zeta functions, but mainly for the related algebro-geometric topological and motivic zeta functions. |
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Keywords: | primary 14B05 32S40 11S80 secondary 14E15 14J17 32S05 |
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