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arXiv · 2004.14683

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

Nicolas Mascot
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Abstract

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.

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Nicolas Mascot. 2020-04-30. Moduli-friendly Eisenstein series over the p-adics and the computation of modular Galois representations. https://arxiv.org/abs/2004.14683

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