Lang's conjecture and sharp height estimates for the elliptic curves y² = x³ + b

Paul Voutier, and Minoru Yabuta. "Lang's conjecture and sharp height estimates for the elliptic curves y² = x³ + b." Acta Arithmetica 173.3 (2016): 197-224. <http://eudml.org/doc/286525>.

@article{PaulVoutier2016,
abstract = {For $E_\{b\}: y² = x³ + b$, we establish Lang’s conjecture on a lower bound for the canonical height of nontorsion points along with upper and lower bounds for the difference between the canonical and logarithmic heights. These results are either best possible or within a small constant of the best possible lower bounds.},
author = {Paul Voutier, Minoru Yabuta},
journal = {Acta Arithmetica},
keywords = {elliptic curve; canonical height; lang's conjecture},
language = {eng},
number = {3},
pages = {197-224},
title = {Lang's conjecture and sharp height estimates for the elliptic curves y² = x³ + b},
url = {http://eudml.org/doc/286525},
volume = {173},
year = {2016},
}

TY - JOUR
AU - Paul Voutier
AU - Minoru Yabuta
TI - Lang's conjecture and sharp height estimates for the elliptic curves y² = x³ + b
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 3
SP - 197
EP - 224
AB - For $E_{b}: y² = x³ + b$, we establish Lang’s conjecture on a lower bound for the canonical height of nontorsion points along with upper and lower bounds for the difference between the canonical and logarithmic heights. These results are either best possible or within a small constant of the best possible lower bounds.
LA - eng
KW - elliptic curve; canonical height; lang's conjecture
UR - http://eudml.org/doc/286525
ER -