9 citations · 9 across the 6 of their papers we have counts for
6 papers
Poincaré series of valuations on functions over a field
Antonio Campillo, Felix Delgado, Sabir Gusein-Zade
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the co…
Real Poincaré series of a plane divisorial valuation
Antonio Campillo, Félix Delgado, Sabir M. Gusein-Zade
Earlier, there was computed the Poincaré series of a valuation or of a collection of valuations on the ring of germs of holomorphic functions in two variables. For a collection of…
On real analogues of the Poincaré series
A. Campillo, F. Delgado, S. M. Gusein-Zade
There exist several equivalent equations for the Poincaré series of a collection of valuations on the ring of germs of functions on a complex analytic variety. We give definitions…
An equivariant Poincaré series of filtrations and monodromy zeta functions
A. Campillo, F. Delgado, S. M. Gusein-Zade
We define a new equivariant (with respect to a finite group action) version of the Poincaré series of a multi-index filtration as an element of the power series ring ${\widetil…
Equivariant Poincare series of filtrations
A. Campillo, F. Delgado, S. M. Gusein-Zade
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 Grothendie…
Poincare series of collections of plane valuations
A. Campillo, F. Delgado, S. M. Gusein-Zade +1
In earlier papers there were given formulae for the Poincare series of multi-index filtrations on the ring of germs of functions of two variables defined by collections of valuatio…