Sabir Gusein-Zade

Poincaré series of valuations on functions over a field

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 coeficients in $\K$. We compute the semigroup Poincaré series and the classical Poincaré series of a valuation.