Special automorphisms on Shimura curves and non-triviality of Heegner points

doi:10.1007/s11425-016-5128-3

CSpace

	Special automorphisms on Shimura curves and non-triviality of Heegner points
	Cai, Li 1; Li YongXiong 2; Wang ZhangJie 1
	2016-07-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	59 期号:7 页码:1307-1326
摘要	We define the notion of special automorphisms on Shimura curves. Using this notion, for a wild class of elliptic curves defined over Q, we get rank one quadratic twists by discriminants having any prescribed number of prime factors. Finally, as an application, we obtain some new results on Birch and Swinnerton-Dyer (BSD) conjecture for the rank one quadratic twists of the elliptic curve X (0)(49).
关键词	Shimura curves Heegner points BSD conjecture
DOI	10.1007/s11425-016-5128-3
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000379083700005
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23059
专题	中国科学院数学与系统科学研究院
通讯作者	Li YongXiong
作者单位	1.Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Cai, Li,Li YongXiong,Wang ZhangJie. Special automorphisms on Shimura curves and non-triviality of Heegner points[J]. SCIENCE CHINA-MATHEMATICS,2016,59(7):1307-1326.
APA	Cai, Li,Li YongXiong,&Wang ZhangJie.(2016).Special automorphisms on Shimura curves and non-triviality of Heegner points.SCIENCE CHINA-MATHEMATICS,59(7),1307-1326.
MLA	Cai, Li,et al."Special automorphisms on Shimura curves and non-triviality of Heegner points".SCIENCE CHINA-MATHEMATICS 59.7(2016):1307-1326.