Mathematical Research Letters
Volume 20 (2013)
Theta lifts and local Maass forms
Pages: 213 – 234
The first two authors and Kohnen have recently introduced a new class of modular objects called locally harmonic Maass forms, which are annihilated almost everywhere by the hyperbolic Laplacian operator. In this paper, we realize these locally harmonic Maass forms as theta lifts of harmonic weak Maass forms. Using the theory of theta lifts, we then construct examples of (non-harmonic) local Maass forms, which are instead eigenfunctions of the hyperbolic Laplacian almost everywhere.
theta lifts, harmonic weak Maass forms, locally harmonic Maass forms, local Maass forms, modular forms
2010 Mathematics Subject Classification
11E16, 11F11, 11F25, 11F27, 11F37