Moduli-friendly Eisenstein series over the p-adics and the computation of modular Galois representations
Year: 2022
Type: article
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 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.
Source: Research in Number Theory
Author: Nicolas Mascot
Institution: Trinity College Dublin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,280
OpenAlex ID: W3022319900