Proving modularity for a given elliptic curve over an imaginary quadratic field

We present an algorithm to determine if the L-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and Berger-Harcos (cf. [HST93], [Tay94] and [BH]) we can associate to an automorphic representation a family of compatible p-adic representations. Our algorithm is based on Faltings-Serre's method to prove that p-adic Galois representations are isomorphic.

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Luis Dieulefait, Lucio Guerberoff, Ariel Pacetti
• Keywords: Automorphic Representation, Compatible P-adic Representations, Imaginary Quadratic Field, MOC 2010, Security Privacy