A refinement of Pólya's method to construct Voronoi diagrams for rational functions

Rikard Bögvad, Christian Hägg

Given a complex polynomial $P$ with zeroes $z_1,\dots ,z_d$, we show that the asymptotic zero-counting measure of the iterated derivatives $Q^{(n)},n=1,2,\dots$, where $Q=R/P$…