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

• Autorzy: Paul Voutier , Minoru Yabuta
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11G50: Heights
• 11G05: Elliptic curves over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 3
• Strony: 197-224

Daty

wydano

2016

Twórcy

autor

Paul Voutier

• London, UK

autor

Minoru Yabuta

• Senri High School, 17-1, 2 chome, Takanodai, Suita, Osaka, 565-0861, Japan

Identyfikatory

DOI

10.4064/aa7761-2-2016