Geodesic
Poincar\'e series of filtration associated with Newton diagram and topological types of singularities
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2015), pp. 24-28

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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. 
@article{VMUMM_2015_4_a2,
     author = {G. D. Solomadin},
     title = {Poincar\'e series of filtration associated with {Newton} diagram and topological types of singularities},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {24--28},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_4_a2/}
}
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G. D. Solomadin. Poincar\'e series of filtration associated with Newton diagram and topological types of singularities. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2015), pp. 24-28. http://geodesic.mathdoc.fr/item/VMUMM_2015_4_a2/