On the rank of elliptic curves on Hilbert class field

被引：3

作者：

Templier, Nicolas ^{[1
]}

机构：

[1] Inst Adv Study, Princeton, NJ 08540 USA

来源：

COMPOSITIO MATHEMATICA | 2011年 / 147卷 / 04期

关键词：

automorphic forms; equidistribution; L-functions; Heegner points; elliptic curves; IMAGINARY QUADRATIC FIELDS; CANONICAL HECKE CHARACTERS; LOCAL EPSILON-FACTORS; HEEGNER POINTS; CM-POINTS; QUATERNION ALGEBRAS; SHIMURA CURVES; L-SERIES; EQUIDISTRIBUTION; DERIVATIVES;

D O I：

10.1112/S0010437X10005051

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E/Q be an elliptic curve and let D < 0 be a sufficiently large fundamental discriminant. If E(<(Q)over bar>) contains Heegner points of discriminant D, those points generate a subgroup of rank at least |D|(delta), where delta > 0 is an absolute constant. This result is compatible with the Birch and Swinnerton-Dyer conjecture.

引用

页码：1087 / 1104

页数：18

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