HEEGNER POINTS ON MODULAR CURVES

被引：7
作者：
Cai, Li [1 ]
Chen, Yihua [2 ]
Liu, Yu [1 ]
机构：
[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
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 370卷 / 05期
基金：
中国博士后科学基金;
关键词：
ADIC L-FUNCTIONS; NONVANISHING THEOREMS; CONGRUENT NUMBERS; QUADRATIC TWISTS; ELLIPTIC-CURVES; L-SERIES; DERIVATIVES; FORMS; GL(2);
D O I：
10.1090/tran/7053
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the Heegner points on more general modular curves other than X-0(N), which generalizes Gross' work "Heegner points on X-0(N)". The explicit Gross-Zagier formula and the Euler system property are stated in this case. Using such a kind of Heegner points, we construct certain families of quadratic twists of X-0(36), with the ranks of Mordell-Weil groups being zero and one respectively, and show that the 2-part of their BSD conjectures hold.
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页码：3721 / 3743
页数：23
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