Theta lifts and local Maass forms
Number Theory
2012-09-25 v1
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
Cite
@article{arxiv.1209.5163,
title = {Theta lifts and local Maass forms},
author = {Kathrin Bringmann and Ben Kane and Maryna Viazovska},
journal= {arXiv preprint arXiv:1209.5163},
year = {2012}
}