Super-replicable functions ${\cal N}(j_{1,N})$ and periodically vanishing property

TL;DR

This paper introduces generalized super-replication formulas and uses them to demonstrate a periodically vanishing property in the Fourier coefficients of a specific Hauptmodul, expanding understanding of super-replicable functions.

Contribution

The paper develops generalized super-replication formulas and applies them to establish a periodically vanishing property in Fourier coefficients of a Hauptmodul.

Findings

Derived super-replication formulas generalizing previous results

Established periodically vanishing Fourier coefficients for ${ m N}(j_{1,12})$

Enhanced understanding of super-replicable functions and their properties

Abstract

We find the super-replication formulae which would be a generalization of replication formulae. And we apply the formulae to derive periodically vanishing property in the Fourier coefficients of the Hauptmodul ${\cal N}(j_{1,12})$ as a super-replicable function.