# Meromorphic modular forms with rational cycle integrals

## TL;DR

This paper investigates the rationality of cycle integrals of meromorphic modular forms linked to quadratic forms, providing explicit rational formulas for certain linear combinations of these integrals.

## Contribution

It introduces finite rational formulas for cycle integrals of meromorphic modular forms associated with quadratic forms, advancing understanding of their rationality properties.

## Key findings

- Finite rational formulas for cycle integrals derived
- Rationality properties of meromorphic modular forms established
- Explicit formulas for linear combinations of cycle integrals provided

## Abstract

We study rationality properties of geodesic cycle integrals of meromorphic modular forms associated to positive definite binary quadratic forms. In particular, we obtain finite rational formulas for the cycle integrals of suitable linear combinations of these meromorphic modular forms.