The notion of integration with respect to the Euler characteristic and its generalizations are
discussed: integration over the infinite-dimensional spaces of arcs and functions, motivic …

A multi-index filtration on the ring of germs of functions can be described by its Poincaré
series. We consider a finer invariant (or rather two invariants) of a multi-index filtration than …

For a reducible curve singularity embedded in a rational surface singularity the Poincaré
series is computed. Here the Poincaré series is defined by the multi-index filtration on the …

Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field
of characteristic p big enough. Given a local ring Op, x at a rational singular point P of X, we …

In earlier papers there were given formulae for the Poincaré series of multi-index filtrations
on the ring of germs of functions of two variables defined by collections of valuations …

Let a finite group $ G $ act on the complex plane $({\Bbb C}^ 2, 0) $. We consider multi-
index filtrations on the spaces of germs of holomorphic functions of two variables equivariant …

We offer a new approach to a definition of an equivariant version of the Poincaré series. This
Poincaré series is defined not as a power series, but as an element of the Grothendieck ring …

We define a new equivariant (with respect to a finite group GG action) version of the
Poincaré series of a multi-index filtration as an element of the power series ring A (G) t_1 …

The aim of this paper is to show the relation between the zeta function introduced by Stöhr
and the Poincaré series of a curve singularity introduced by Campillo, Delgado and Gusein …

Let O be an equicharacteristic reduced complete noetherian local ring of Krull dimension
one, and let S be the value semigroup associated with O. The aim of the paper is to …