On the polar quotients of an analytic plane curve
Let \(f \in \mathbb{C}\{x,y\}\) be a reduced power series and \(t\) a power series of order 1 not dividing \(f\). The polar quotients of \(f\) with respect to \(t\) are defined by \[ Q(f,t) = \left\{\frac{(f,\varphi)_0}{(t,\varphi)_0} \Bigg|\varphi \text{ an irreducible factor of } \frac{\partial(t,f)}{\partial(x,y)}\right\}, \] here \((f,\varphi)_0\) is the intersection multiplicity of \(f\) and \(\varphi\) at 0. An explicit formula in terms of characteristic exponents and intersection multiplicities of the branches for the polar quotients is given.
scientific article; zbMATH DE number 1782966