18 citations · 48 across the 11 of their papers we have counts for
6 papers · 1 filter
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 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…
A finiteness property of torsion points
Matthew Baker, Su-Ion Ih, Robert Rumely
Let k be a number field, let E/k be an elliptic curve, and let S be a finite set of places of k contianing the archimedean places. Let F be an algebraic closure of k. We prove that…
Analysis and dynamics on the Berkovich projective line
Robert Rumely, Matthew Baker
This is a set of expanded lecture notes from the Berkovich Space seminar held at the University of Georgia during Spring, 2004. The purpose of the notes is to provide a non-technic…
Equidistribution of small points, rational dynamics, and potential theory
Matthew Baker, Robert Rumely
If phi(z) is a rational function on P^1 of degree at least 2 with coefficients in a number field k, we compute the homogeneous transfinite diameter of the v-adic filled Julia sets…