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Coulomb-gas representation of minimal models on Riemann surfaces.

In this paper we use the Coulomb-gas approach to construct the minimal-model partition function and correlation functions on Riemann surfaces. The background-charge term in the action of the nonchiral scalar field is carefully studied and the various modular-invariant partition functions are shown to be reproducible from a treatment of this term. These results can be understood as a generalization of those of the microscopic lattice-model approach.