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Lang’s conjecture and sharp height estimates for the elliptic curves $y^{2}=x^{3}+b$

Volume 173 / 2016

Paul Voutier, Minoru Yabuta Acta Arithmetica 173 (2016), 197-224 MSC: 11G05, 11G50. DOI: 10.4064/aa7761-2-2016 Published online: 11 May 2016


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


  • Paul VoutierLondon, UK
  • Minoru YabutaSenri High School
    17-1, 2 chome, Takanodai, Suita
    Osaka, 565-0861, Japan

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