String couplings from meromorphic differentials

The ''Neumann-function method'' which allows one to determine oscillator representation of multiple string vertices is put on a firm basis. The Neumann coefficients are related to the Laurent coefficients of certain meromorphic differentials. A systematic procedure of constructing the differentials is developed. The method is exemplified by the ''covariantized'' light-cone vertex. Our results on the ghost part of this vertex are in disagreement with various proposals in the literature. (orig.)