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Computing Galois representations of modular abelian surfaces

Part of: Computational number theory Discontinuous groups and automorphic forms Arithmetic algebraic geometry

Published online by Cambridge University Press:  01 August 2014

Jinxiang Zeng
Jinxiang Zeng*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China email cengjx09@mails.tsinghua.edu.cn

Abstract

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Let $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}f\in S_2(\Gamma _0(N))$ be a normalized newform such that the abelian variety $A_f$ attached by Shimura to $f$ is the Jacobian of a genus-two curve. We give an efficient algorithm for computing Galois representations associated to such newforms.

MSC classification

Secondary: 11Y40: Algebraic number theory computations 11F80: Galois representations 11G18: Arithmetic aspects of modular and Shimura varieties 11G20: Curves over finite and local fields
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Special Issue A: Algorithmic Number Theory Symposium XI , 2014 , pp. 36 - 48
Copyright
© The Author 2014 

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