17 citations · 50 across the 11 of their papers we have counts for
10 papers · 1 filter
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…
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…
Equidistribution of small subvarieties of an abelian variety
Matthew Baker, Su-ion Ih
We prove an equidistribution result for small subvarieties of an abelian variety which generalizes the Szpiro-Ullmo-Zhang theorem on equidistribution of small points.
A Lower Bound for the Canonical Height on Abelian Varieties over Abelian Extensions
Matthew Baker, Joseph Silverman
Let A be an abelian variety defined over a number field K, and consider the canonical height function attached to a symmetric ample line bundle L on A. We prove that there is a pos…