论文标题
对P-ADIC的模量友好的Eisenstein系列和模块化Galois表示的计算
Moduli-friendly Eisenstein series over the p-adics and the computation of modular Galois representations
论文作者
论文摘要
我们展示了如何计算出在代数曲线雅各布人扭转中发生的galois表示的方法，可以适应模块化曲线。主要成分是使用Makdisi引入的“对模量友好”的Eisenstein系列，这使我们能够在模块化曲线点的P-ADIC上评估模块化形式，并分配我们需要模块化曲线方程和Q-Expansion Computions。所得算法与复杂的分析方法相比非常有利。
We show how our p-adic method to compute Galois representations occurring in the torsion of Jacobians of algebraic curves can be adapted to modular curves. The main ingredient is the use of "moduli-friendly" Eisenstein series introduced by Makdisi, which allow us to evaluate modular forms at p-adic of modular curves points and dispenses us of the need for equations of modular curves and for q-expansion computations. The resulting algorithm compares very favourably to the complex-analytic method.
