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

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

2011-04-24

arxiv.org/abs/1104.4645v2

Mathematics

Number Theory

include results for the difference between the canonical and the logarithmic height too

Scientific paper

For $E_{a}: y^{2}=x^{3}+ax$, 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.

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