Cycle integrals of meromorphic modular forms and coefficients of harmonic Maass forms

TL;DR

This paper explores the relationship between cycle integrals of meromorphic modular forms and harmonic Maass forms, providing explicit formulas through regularised theta lifts to deepen understanding of their coefficients.

Contribution

It introduces explicit formulas connecting cycle integrals of meromorphic modular forms with harmonic Maass form coefficients via regularised theta lifts.

Findings

Derived explicit formulas for cycle integrals in terms of harmonic Maass form coefficients

Established a connection between meromorphic modular forms and harmonic Maass forms

Enhanced understanding of the structure of modular forms through theta lifts

Abstract

In this paper, we investigate traces of cycle integrals of certain meromorphic modular forms. By relating them to regularised theta lifts we provide explicit formulae for them in terms of coefficients of harmonic Maass forms.