On the Average Value of the Canonical Height in Higher Dimensional Families of Elliptic curves
Abstract
Given an elliptic curve E over a function field K=Q(T1,...,Tn), we study the behavior of the canonical height h(Ew) of the specialized elliptic curve Ew with respect to the height of w in Qn. In this paper, we prove that there exists a uniform non-zero lower bound for the average of the quotient h(Ew)(Pw)/h(w) for all non-torsion P in E(K).
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