Rank-one quadratic twists of an infinite family of elliptic curves

被引：11
|
作者：
Byeon, Dongho [1 ]
Jeon, Daeyeol [2 ]
Kim, Chang Heon [3 ]
机构：
[1] Seoul Natl Univ, Dept Math, Seoul, South Korea
[2] Kongju Natl Univ, Dept Math Educ, Kong Ju 314701, South Korea
[3] Hanyang Univ, Dept Math, Seoul 133791, South Korea
来源：
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2009年 / 633卷
关键词：
MODULAR L-FUNCTIONS; L-SERIES; POINTS;
D O I：
10.1515/CRELLE.2009.060
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A conjecture of Goldfeld implies that a positive proportion of quadratic twists of an elliptic curve E/Q has (analytic) rank 1. This assertion has been confirmed by Vatsal [V1] and the first author [By] for only two elliptic curves. Here we confirm this assertion for infinitely many elliptic curves E/Q using the Heegner divisors, the 3-part of the class groups of quadratic fields, and a variant of the binary Goldbach problem for polynomials.
引用
收藏
页码：67 / 76
页数：10
相关论文
共 42 条
12345