Theta liftings on weak Maass forms

TL;DR

This paper develops a method to lift weak Maass forms of half-integral weight to even integral weight forms using regularized theta integrals, extending Niwa's theta liftings to harmonic weak Maass forms.

Contribution

It introduces a new theta lifting technique for weak Maass forms, generalizing Niwa's liftings to a broader class of harmonic weak Maass forms.

Findings

Constructed theta liftings from half-integral to even integral weight weak Maass forms.

Extended Niwa's theta liftings to harmonic weak Maass forms.

Obtained results analogous to Niwa's in this broader context.

Abstract

We construct theta liftings from half-integral weight weak Maass forms to even integral weight weak Maass forms by using regularized theta integral. Moreover it gives an extension of Niwa's theta liftings on harmonic weak Maass forms. And we obtain the similar results to those by Niwa.