We introduce a general strategy for proving quantitative and uniform bounds on the number
of common points of height zero for a pair of inequivalent height functions on P^1(Q). We …

Let K be a function field, let φ∈ K (T) be a rational map of degree d≧ 2 defined over K, and
suppose that φ is not isotrivial. In this paper, we show that a point P∈ ℙ 1 () has φ-canonical …

Let E be an elliptic curve defined over Q without complex multiplication. The field F
generated over Q by all torsion points of E is an infinite, nonabelian Galois extension of the …

In the context that arose from an old problem of Lang regarding the torsion points on
subvarieties of G md, we describe the points that lie in a given variety, are defined over the …

We show that every sequence of torsion-free arithmetic congruence lattices in PGL (2, R)
PGL (2, R) or PGL (2, C) PGL (2, C) satisfies a strong quantitative version of the limit …

arxiv:math/0507484v4 [math.NT] 31 May 2006 Page 1 arxiv:math/0507484v4 [math.NT] 31
May 2006 A LOWER BOUND FOR AVERAGE VALUES OF DYNAMICAL GREEN’S …

For an algebraic number $\alpha $, let $ h (\alpha) $ denote its logarithmic Weil height. In
2002, Bombieri and Zannier obtained lower bounds for Weil height for totally $ p $-adic …

Let E/k be an elliptic curve over a number field. We obtain some quantitative refinements of
results of Hindry-Silverman, giving an upper bound for the number of k-rational torsion …

We give a conditional proof of the Uniform Boundedness Conjecture of Morton and
Silverman in the case of polynomials over number fields, assuming a standard conjecture in …

We study the behavior of canonical height functions $\widehat {h} _f $, associated to rational
maps $ f $, on totally $ p $-adic fields. In particular, we prove that there is a gap between …