A classification of harmonic weak Maass forms of half-integral weight

• 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.

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NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Primary: 11F12

Secondary: 11F27

11F70

modular-forms

cm values

coefficients

formulas

series

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Mathematics

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