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.
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页码：1087 / 1104
页数：18
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