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On the Average Value of the Canonical Height in Higher Dimensional Families of Elliptic curves (1305.7207v4)

Published 30 May 2013 in math.AG and math.NT

Abstract: Given an elliptic curve E over a function field K=Q(T_1,...,T_n), we study the behavior of the canonical height ^h_(E_w) of the specialized elliptic curve E_w with respect to the height of w in Q^n. In this paper, we prove that there exists a uniform non-zero lower bound for the average of the quotient ^{h_(E_w)(P_w)/h(w)} for all non-torsion P in E(K).