Geodesic
Lang’s conjecture and sharp height estimates for the elliptic curves $y^{2}=x^{3}+b$
Paul Voutier1 ; Minoru Yabuta2
1London, UK
2Senri High School 17-1, 2 chome, Takanodai, Suita Osaka, 565-0861, Japan
Acta Arithmetica, Tome 173 (2016) no. 3, pp. 197-224
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa7761-2-2016
Keywords: establish lang conjecture lower bound canonical height nontorsion points along upper lower bounds difference between canonical logarithmic heights these results either best possible within small constant best possible lower bounds

Paul Voutier  1   ; Minoru Yabuta  2

1 London, UK
2 Senri High School 17-1, 2 chome, Takanodai, Suita Osaka, 565-0861, Japan 
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     title = {Lang{\textquoteright}s conjecture and sharp height estimates for the elliptic curves $y^{2}=x^{3}+b$},
     journal = {Acta Arithmetica},
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Paul Voutier; Minoru Yabuta. Lang’s conjecture and sharp height estimates for the elliptic curves $y^{2}=x^{3}+b$. Acta Arithmetica, Tome 173 (2016) no. 3, pp. 197-224. doi: 10.4064/aa7761-2-2016

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