17 citations · 50 across the 11 of their papers we have counts for
12 papers
Global discrepancy and small points on elliptic curves
Matthew Baker, Clayton Petsche
Let E be an elliptic curve defined over a number field k. In this paper, we define the ``global discrepancy'' of a finite set Z of algebraic points on E which in a precise sense me…
A lower bound for average values of dynamical Green's functions
Matthew Baker
We provide a Mahler/Elkies-style lower bound for the average values of dynamical Green's functions on the projective line over an arbitrary valued field, and give some dynamical an…
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…
Metrized graphs, electrical networks, and Fourier analysis
Matthew Baker, Xander Faber
A metrized graph is a finite weighted graph whose edges are thought of as line segments. In this expository paper, we study the Laplacian operator on a metrized graph and some impo…
Harmonic analysis on metrized graphs
Matthew Baker, Robert Rumely
We study the Laplacian on a metrized graph, and its eigenfunctions.
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…