Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition

2012/07/24 by Kathrin Bringmann, Bringmann, Kathrin, Martin Raum +4
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1207.5600

24 pages, To appear in Transactions of the AMS

openalex publication_date 2012/07/24 · arxiv created 2014/03/24 · arxiv updated 2014/03/25 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Real-analytic Jacobi forms play key roles in different areas of mathematics and physics, but a satisfactory theory of such Jacobi forms has been lacking. In this paper, we fill this gap by introducing a space of harmonic Maass-Jacobi forms with singularities which includes the real-analytic Jacobi forms from Zwegers's PhD thesis. We provide several structure results for the space of such Jacobi forms, and we employ Zwegers's \widehatμ-functions to establish a theta-like decomposition.

Citations

• A Serre derivative for even weight Jacobi Forms
• On two geometric theta lifts

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