Dieulefait, L;
Guerberoff, L;
Pacetti, A;
(2010)
Proving modularity for a given elliptic curve over an imaginary quadratic field.
Mathematics of Computation
, 79
pp. 1145-1170.
10.1090/S0025-5718-09-02291-1.
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Abstract
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. \cite{harris-taylor}, \cite{taylorII} and \cite{berger-harcos}) 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: | Article |
|---|---|
| Title: | Proving modularity for a given elliptic curve over an imaginary quadratic field |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/S0025-5718-09-02291-1 |
| Publisher version: | https://doi.org/10.1090/S0025-5718-09-02291-1 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | 11F80; 11G05 |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1474963 |
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