A classification of harmonic weak Maaß forms of half-integral weight
Journal article, 2023

We classify Harish-Chandra modules generated by the pullback to the metaplectic group of harmonic weak Maaß 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 Maaß 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.


Claudia Alfes-Neumann

Bielefeld University

Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

Research in Number Theory

23639555 (eISSN)

Vol. 9 3 48

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Swedish Research Council (VR) (2019-03551), 2020-01-01 -- 2023-12-31.

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Swedish Research Council (VR) (2015-04139), 2016-01-01 -- 2019-12-31.

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