2019/06/12 by Trevor J. Richards, Richards, Trevor J.
Mathematics · #30C15 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30C15
paper · pdf · doi:10.48550/arxiv.1906.05262
arxiv created 2019/06/12 · arxiv updated 2019/06/13
In this note, we use Rouché's theorem and the pleasant properties of the arithmetic of the logarithmic derivative to establish several new results regarding the geometry of the zeros, poles, and critical points of a rational function. Included is an improvement on a result by Alexander and Walsh regarding the distance from a given zero or pole of a rational function to the nearest critical point.