论文标题
椭圆形曲线的模块化，元素$ \ mathbb {z} _p $ - 真实二次字段的扩展
Modularity of elliptic curves over cyclotomic $\mathbb{Z}_p$-extensions of real quadratic fields
论文作者
论文摘要
我们证明，在循环$ \ mathbb {z} _p $ - 真实二次场的扩展是模块化的所有椭圆曲线都是模块化的，假设是扭曲$ l $ luncunction的代数部分的代数部分是$ p $ p $ addic单位。我们的结果是X. Zhang的结果的概括，这是Thorne结果的真正二次类似物。
We prove that all elliptic curves defined over the cyclotomic $\mathbb{Z}_p$-extension of a real quadratic field are modular under the assumption that the algebraic part of the central value of a twisted $L$-function is a $p$-adic unit. Our result is a generalization of a result of X. Zhang, which is a real quadratic analogue of a result of Thorne.
