A classification of harmonic weak Maa{\ss} forms of half-integral weight
Number Theory
2022-02-03 v1
Abstract
We classify Harish-Chandra modules generated by the pullback to the metaplectic group of harmonic weak Maa{\ss} forms with exponential growth allowed at the cusps. This extends work by Schulze-Pillot and parallels recent work by Bringmann-Kudla, who investigated the case of integral weights. We realize each of our cases via a regularized theta lift of an integral weight harmonic weak Maa{\ss} form. Harish-Chandra modules in both integral and half-integral weight that occur need not be irreducible. Therefore, our display of the role that the theta lifting takes in this picture, we hope, contributes to an initial understanding of a theta correspondence for extensions of Harish-Chandra modules.
Keywords
Cite
@article{arxiv.2202.00744,
title = {A classification of harmonic weak Maa{\ss} forms of half-integral weight},
author = {Claudia Alfes-Neumann and Martin Raum},
journal= {arXiv preprint arXiv:2202.00744},
year = {2022}
}