On Zariski's multiplicity conjecture

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We discuss some features of the so-called Zariski's multiplicity problem especially the application of the work of A'Campo on the zeta function of a monodromy of an isolated singularity of a complex hypersurface to the problem.
13 pages. To appear in Proceedings volume "Traces in Geometry, Number Theory and Quantum Fields", S. Albeverio, M. Marcolli, S. Paycha eds

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