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On Serreʼs conjecture over imaginary quadratic fields
Journal article   Peer reviewed

On Serreʼs conjecture over imaginary quadratic fields

Journal of number theory, Vol.132(4), pp.637-656
04/01/2012

Abstract

Galois representation Hecke operator Modular form Serreʼs conjecture Number Theory
We study an analog of Serreʼs conjecture over imaginary quadratic fields. In particular, we ask whether the weight recipe of Buzzard, Diamond and Jarvis will hold in this setting. Using a program written by the author, we provide computational evidence that this is in fact the case. In order to justify the method used in the program, we prove that a modular symbols method will work for arbitrary weights over imaginary quadratic fields.

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