Points of small height on elliptic curves

[摘要] We study lower bounds for the Neron-Tate height of a (Q) over bar-rational point P of infinite order of an elliptic curve E over (Q) over bar. This work, which follows a previous work by the author, shows that another transcendence construction, which is a variant of a proof introduced by D. Masser (1989) gives sharper bounds than those proved in (David, 1992), provided that one works not only at several places of multiplicative type bad reduction simultaneously but also uses the periodicity of the elliptic functions associated with a (suitable) model of the given curve as in (David, 1992). It is also remarked that the approach of M. Hindry and J. Silverman (1990) leads essentially to the same bounds. Asa corollary, one obtains that the ''5th successive minimum'' tends to infinity with the height of the curve. (C) 1997 Academic Press.

[发布日期] 1997-05-01