Lang's Conjecture and Sharp Height Estimates for the elliptic curves $y^{2}=x^{3}+ax$

Paul Voutier; Minoru Yabuta

doi:10.1142/S1793042113500176

Lang's Conjecture and Sharp Height Estimates for the elliptic curves $y^{2}=x^{3}+ax$

Number Theory 2013-07-18 v4

Authors: Paul Voutier , Minoru Yabuta

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Abstract

For elliptic curves given by the equation $E_{a}: y^{2}=x^{3}+ax$ , we establish the best-possible version of Lang's conjecture on the lower bound of the canonical height of non-torsion points along with best-possible upper and lower bounds for the difference between the canonical and logarithmic height.

Keywords

Lang's conjecture canonical height elliptic curves height estimates non-torsion points logarithmic height

Cite

@article{arxiv.1104.4645,
  title  = {Lang's Conjecture and Sharp Height Estimates for the elliptic curves $y^{2}=x^{3}+ax$},
  author = {Paul Voutier and Minoru Yabuta},
  journal= {arXiv preprint arXiv:1104.4645},
  year   = {2013}
}

Comments

published version. Lemmas 5.1 and 6.1 now precise (with resultant refinement to Theorem 1.2). Small corrections too

Lang's Conjecture and Sharp Height Estimates for the elliptic curves $y^{2}=x^{3}+ax$

Abstract

Keywords

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