Moduli-friendly Eisenstein series over the p-adics and the computation of modular Galois representations

被引：0

作者：

Nicolas Mascot

机构：

[1] Trinity College,

来源：

Research in Number Theory | 2022年 / 8卷

关键词：

Modular form; Galois representation; Jacobian; -Adic; Moduli; Algorithm; 11F80; 11Y40; 14H40; 14G20; 14G35; 11G18; 11F11;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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 points of modular curves and dispenses us of the need for equations of modular curves and for q-expansion computations in the construction of models of modular Jacobians. The resulting algorithm compares very favourably to our complex-analytic method.

引用

共 12 条

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