Regularized Pairings of Meromorphic Modular Forms and Theta Lifts

TL;DR

This paper demonstrates that certain meromorphic modular forms can be derived from regularized theta lifts of Poincaré series, simplifying their pairing evaluations and advancing understanding of their structure.

Contribution

It introduces a new method to obtain meromorphic modular forms via regularized theta lifts, linking them to Poincaré series and weight raising operators.

Findings

Meromorphic modular forms are images of regularized theta lifts.

Simplified evaluation of regularized pairings with other modular forms.

Provides a new perspective on the structure of these modular forms.

Abstract

We show that the meromorphic modular forms recently considered by Bringmann and Kane can be obtained as images of regularized theta lifts of Poincar\'{e} series under weight raising operators. We use this fact in order to simplify the evaluation of the regularized pairing, also defined by Bringmann and Kane, of these functions with other meromorphic modular forms.