Non-vanishing Theorems for Quadratic Twists of Elliptic Curves
Non-vanishing Theorems for Quadratic Twists of Elliptic Curves
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DOI：
10.4310/ajm.2016.v20.n3.a4
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发表时间：
2014-08
期刊：
影响因子：
--
通讯作者：
Shuai Zhai
中科院分区：
文献类型：
--
作者：
Shuai Zhai
在本文中，我们表明，通过应用模符号的一些结果，对于一个家庭的某些椭圆曲线定义在$\mathbb Q$，有一个大类的显式二次扭曲的复杂$L$-系列不为零，在$s=1$，并为2 $-部分的Birch-Swinnerton-Dyer猜想成立。
In this paper, we show that, by applying some results on modular symbols, for a family of certain elliptic curves defined over $\mathbb Q$, there is a large class of explicit quadratic twists whose complex $L$-series does not vanish at $s=1$, and for which the $2$-part of Birch-Swinnerton-Dyer conjecture holds.