• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.343-371
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• 2007

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