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# Mathematical Research Letters

## Volume 20 (2013)

### Number 2

### Theta lifts and local Maass forms

Pages: 213 – 234

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n2.a2

#### Authors

#### Abstract

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.

#### Keywords

theta lifts, harmonic weak Maass forms, locally harmonic Maass forms, local Maass forms, modular forms

#### 2010 Mathematics Subject Classification

11E16, 11F11, 11F25, 11F27, 11F37

Published 3 December 2013