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

Wei Pin Wong. "On the average value of the canonical height in higher dimensional families of elliptic curves." Acta Arithmetica 166.2 (2014): 101-128. <http://eudml.org/doc/279115>.

@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 -