On the average value of the canonical height in higher dimensional families of elliptic curves

@article{WeiPinWong2014,
abstract = {Given an elliptic curve E over a function field K = ℚ(T₁,...,Tₙ), we study the behavior of the canonical height $ĥ_\{E_ω\}$ of the specialized elliptic curve $E_ω$ with respect to the height of ω ∈ ℚⁿ. We prove that there exists a uniform nonzero lower bound for the average of the quotient $(ĥ_\{E_ω\}(P_ω))/h(ω)$ over all nontorsion P ∈ E(K).},
author = {Wei Pin Wong},
journal = {Acta Arithmetica},
keywords = {height function; elliptic curves; function field},
language = {eng},
number = {2},
pages = {101-128},
title = {On the average value of the canonical height in higher dimensional families of elliptic curves},
url = {http://eudml.org/doc/279115},
volume = {166},
year = {2014},
}

TY - JOUR
AU - Wei Pin Wong
TI - On the average value of the canonical height in higher dimensional families of elliptic curves
JO - Acta Arithmetica
PY - 2014
VL - 166
IS - 2
SP - 101
EP - 128
AB - Given an elliptic curve E over a function field K = ℚ(T₁,...,Tₙ), we study the behavior of the canonical height $ĥ_{E_ω}$ of the specialized elliptic curve $E_ω$ with respect to the height of ω ∈ ℚⁿ. We prove that there exists a uniform nonzero lower bound for the average of the quotient $(ĥ_{E_ω}(P_ω))/h(ω)$ over all nontorsion P ∈ E(K).
LA - eng
KW - height function; elliptic curves; function field
UR - http://eudml.org/doc/279115
ER -