Poincaré series of filtration associated with the Newton diagram and topological type of singularity / G. D. Solomadin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 4. P. 24-28 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 171-175].

The Poincaré series of multi-index filtration on the ring of germs defined by S.M. Gusein-Zade and W. Ebeling for the germ of function in terms of its Newton diagram is considered. Examples of functions of two variables are described in the paper. These examples show that the Poincaré series for the germ of function depends not only on the type of the diagram, but also on the germ of the function.

Key words: finite group actions, monodromy zeta-function, monodromy.