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

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 $\mathcal{N}(j_{1,12})$ as a super-replicable function.

34 pages