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

Alfes-Neumann, Claudia; Raum, Martin

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

Alfes-Neumann C, Raum M (2023)
Research in Number Theory 9: 48.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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DOI

https://doi.org/10.1007/s40993-023-00455-9

URN

urn:nbn:de:0070-pub-29610373

Autor*in

Alfes-Neumann, Claudia^UniBi ; Raum, Martin

Einrichtung

Fakultät für Mathematik

Abstract / Bemerkung

Abstract 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

Erscheinungsjahr

2023

Zeitschriftentitel

Research in Number Theory

Band

Seite(n)

Urheberrecht / Lizenzen

Creative Commons Namensnennung 4.0 International Public License (CC-BY 4.0)

eISSN

2363-9555

Finanzierungs-Informationen

Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.

Page URI

https://pub.uni-bielefeld.de/record/2961037

Zitieren

Alfes-Neumann C, Raum M. A classification of harmonic weak Maaß forms of half-integral weight. Research in Number Theory. 2023;9:48.

Alfes-Neumann, C., & Raum, M. (2023). A classification of harmonic weak Maaß forms of half-integral weight. Research in Number Theory, 9, 48. https://doi.org/10.1007/s40993-023-00455-9

Alfes-Neumann, Claudia, and Raum, Martin. 2023. “A classification of harmonic weak Maaß forms of half-integral weight”. Research in Number Theory 9: 48.

Alfes-Neumann, C., and Raum, M. (2023). A classification of harmonic weak Maaß forms of half-integral weight. Research in Number Theory 9, 48.

Alfes-Neumann, C., & Raum, M., 2023. A classification of harmonic weak Maaß forms of half-integral weight. Research in Number Theory, 9, p 48.

C. Alfes-Neumann and M. Raum, “A classification of harmonic weak Maaß forms of half-integral weight”, Research in Number Theory, vol. 9, 2023, pp. 48.

Alfes-Neumann, C., Raum, M.: A classification of harmonic weak Maaß forms of half-integral weight. Research in Number Theory. 9, 48 (2023).

Alfes-Neumann, Claudia, and Raum, Martin. “A classification of harmonic weak Maaß forms of half-integral weight”. Research in Number Theory 9 (2023): 48.

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