On the independence of Heegner points associated to distinct quadratic imaginary fields

[摘要] Let E/Q be an elliptic curve with no CM and a fixed modular parametrization Phi(E): X-0(N) -> E and let P-1,..,P-r is an element of E ((Q) over bar) be Heegner points attached to the rings of integers of distinct quadratic imaginary fields k(1),..., k(r). We prove that if the odd parts of the class numbers of k(1),..., k(r) are larger than a constant C = C(E, Phi(E)) depending only on E and Phi(E), then the points P-1,..., P-r are independent in E((Q) over bar)/E-tors. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-01

[关键词] elliptic curve;heegner point;quadratic imaginary field