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

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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.
34 pages

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