The degenerate parts of spaces of meromorphic cusp forms under a regularized inner product

TL;DR

This paper studies the inner product structure of spaces of meromorphic cusp forms, focusing on degenerate parts and quotient spaces, to better understand their mathematical properties.

Contribution

It provides explicit computations of degenerate components and inner products on quotient spaces of meromorphic cusp forms.

Findings

Identification of degenerate parts in spaces of meromorphic cusp forms

Explicit inner product calculations on quotient spaces

Enhanced understanding of the structure of these modular form spaces

Abstract

We investigate the inner product between meromorphic modular forms from certain distinguished subspaces. In particular, we compute the degenerate parts of these subspaces and further compute the inner product on some of the remaining quotient spaces.