18 citations · 48 across the 11 of their papers we have counts for
11 papers
The Lipschitz Constant of a Nonarchimedean Rational Function
Robert Rumely, Stephen Winburn
Let K be a complete, algebraically closed nonarchimedean valued field, and let f(z) be a non-constant rational function in K(z). We provide explicit bounds for the Lipschitz consta…
Configuration of the Crucial Set for a Quadratic Rational Map
John R. Doyle, Kenneth Jacobs, Robert Rumely
Let be a complete, algebraically closed non-archimedean valued field, and let have degree two. We describe the crucial set of in terms of the multipliers of…
The Geometry of the Minimal Resultant Locus
Robert Rumely
Let K be a complete, algebraically closed, nonarchimedean valued field, and let f(z) be a rational function in K(z) of degree d at least 2. We show there is a natural way to assign…
The Minimal Resultant Locus
Robert Rumely
Let K be a complete, algebraically closed nonarchimedean valued field, and let f(z) in K(z) be a rational function of degree d at least 2. We give an algorithm to determine whether…
The Fekete-Szego theorem with Local Rationality Conditions on Curves
Robert Rumely
Let be a number field or a function field in one variable over a finite field, and let be a separable closure of . Let be a smooth, complete, connected curve…
Transfinite diameter and the resultant
Laura DeMarco, Robert Rumely
We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E in C^N by a regular polynomial map F, expressing it in terms of the resultant of the leading…