$\Gamma_{1}(N)$-Analogues of the Monster Denominator Formula

TL;DR

This paper develops analogues of the monster denominator formula for the modular group (N), extending the classical theory to a broader class of modular forms and groups.

Contribution

It introduces (N)-analogues of the monster denominator formula, expanding the understanding of modular forms related to the monster group.

Findings

Established (N)-analogues of the monster denominator formula

Extended classical modular form theory to new groups

Provided foundational results for further research in moonshine phenomena

Abstract

In this note, we establish $\Gamma_{1}(N)$-analogues for the monster denominator formula.