A lower bound for the canonical height on elliptic curves over abelian extensions

JOURNAL OF NUMBER THEORY

卷:104

Article

Silverman, JH

关键词: elliptic curve;    canonical height;    Lehmer conjecture;   

DOI  :  10.1016/j.jnt.2003.07.001

来源: Elsevier

【 摘 要 】

Let E/K be an elliptic curve defined over a number field, let (h) over cap be the canonical height on E, and let K-ab/K be the maximal abelian extension of K. Extending work of M. Baker (IMRN 29 (2003) 1571-1582), we prove that there is a constant C(E/K) > 0 so that every nontorsion point P is an element of E(K-ab) satisfies (h) over cap (P) > C(E/K). (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free