Место издания:Ministry of Education of the Republic of Azerbaijan Baku, Azerbaijan
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Аннотация:There are a number of observations when Poincare series of natural filtrations on rings of germs of functions are related (sometimes coincide) with certain monodromy zeta functions. These relations are
not really understood. They are obtained by direct computations of their sides in one and the same
terms and comparison of the obtained results. The definition of the Poincare series of a multi-index
filtration is related with the notion of integration with respect to the Euler characteristic over the
projectivization of the ring of germs of functions (which is an infinite dimensional space). Integration
with respect to the Euler characteristic is also a useful tool for computing Poincare series and mon-
odromy zeta functions. There were discussed the basic notions and statements and also some recent results.