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Date
2019-08-01
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Muto, Narita and Pitale construct counterexamples to the Generalized Ramanujan Conjecture for GL(2,B) over the division quaternion algebra B with discriminant two via a lift from SL(2). In this dissertation, I characterize the image of this lift in terms of the Fourier coefficients. The previous methods of Maass, Kohnen or Kojima do not apply here, hence I approached this problem via a combination of classical and representation theory techniques to identify the image. Crucially, I used the Jacquet Langlands correspondence described by Badulescu and Renard to characterize the representations.
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Number Theory, Automorphic forms, Representation Theory, Maass forms