Abstract
We address the concrete spectral analysis of an invariant magnetic Schrödinger operator, which acts on one-dimensional \(L^2\)-mixed automorphic functions associated with a given equivariant pair \((\rho , \tau )\) and a discrete subgroup of the semi-direct group \(\textsf{U}(1) \ltimes \mathbb {C}\). To achieve this, we employ a lifting theorem to the classical automorphic functions associated with a specific pseudo-character. In addition, we offer a partial characterization of the equivariant pairs relative to our setting and discuss possible generalization to higher dimensions.
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Acknowledgements
The authors are grateful for the valuable discussions and support from the members of the “Ahmed Intissar” and “Analysis, P.D.E.& Spectral Geometry” seminars.
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El Fardi, A., Ghanmi, A. & Imlal, L. A lifting theorem for planar mixed automorphic functions. Ramanujan J 64, 289–307 (2024). https://doi.org/10.1007/s11139-024-00830-9
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DOI: https://doi.org/10.1007/s11139-024-00830-9