Diophantine Problems on Elliptic Curves

(Un exposé de Noriko Hirata au séminaire de théorie des nombres de Chevaleret le 29 juin 2000)

Résumé :

We give here an estimate of lower bound for linear forms in logarithms associated with elliptic curves defined over a number field. This is a joint work with Sinnou David of Paris 6 University. Our result shows the best possible estimate concerning with height of coefficients of the linear forms, not necessarily on elliptic curves with complex multiplication. Our main idea comes from a variable change considered by G.~V. Chudnovsky in the late 70's.