论文标题
平衡三重产品的近似$ P $ -ADIC $ L $ - 功能
Approximations of the balanced triple product $p$-adic $L$-function
论文作者
论文摘要
本注释的主要目的是提供一种算法，用于近似于[HSI21]中构建的平衡$ p $ p $ - ad-adic $ l $ function，该算法在$（2,1,1）$中构建，该点位于插值区域之外。算法过程是在[FM14]的工作上建立的，并考虑了$ GL_2（\ Mathbb {Q} _P）$的Bruhat--------------------------我们对至少一个HIDA家族与理由的椭圆曲线相关联的情况很感兴趣，并且我们将自己进一步限制为仅一个有限的局部功能方程符号为$ -1 $。
The main purpose of this note is to provide an algorithm for approximating the value of the balanced $p$-adic $L$-function, as constructed in [Hsi21], at the point $(2,1,1)$, which is lying outside of the interpolation region. The algorithmic procedure is obtained building on the work of [FM14] and considering finite length geodesics on the Bruhat--Tits tree for $GL_2(\mathbb{Q}_p)$. We are interested in the case where at least one of the Hida families is associated with an elliptic curve over the rationals and we further restrict ourselves to the case where only one finite local sign of the functional equation is $-1$.
