Isomorphism of Skew-Holomorphic Harmonic Maass-Jacobi Forms and Certain Weak Harmonic Maass Forms

TL;DR

This paper establishes an isomorphism between certain harmonic Maass forms and skew-holomorphic harmonic Maass-Jacobi forms, extending the understanding of their structure and relationships in the context of modular forms.

Contribution

It proves an isomorphism linking Kohnen's plus space harmonic Maass forms and skew-holomorphic harmonic Maass-Jacobi forms for specific weights and indices.

Findings

Proves isomorphism for weight k-1/2 harmonic Maass forms and skew-holomorphic harmonic Maass-Jacobi forms.

Extends the theory of harmonic Maass forms and Jacobi forms.

Clarifies the structure of these spaces in the case of prime indices.

Abstract

Recently Bringmann, Raum and Richter generalised the definition of Jacobi forms and Skoruppa's skew-holomorphic Jacobi forms by intertwining with harmonic Maass forms. We prove the isomorphism of the Kohnen's plus space analogue of harmonic Maass forms of weight $k-1/2$ for $\Gamma_0(4m)$ and the space of these skew-holomorphic harmonic Maass-Jacobi forms of weight $k$ and index $m$ for $k$ odd and $m=1$ or a prime.