Abstract
In this paper, we present a general solution of the scalar Riemann problem on a closed Riemann surface in the case of a compound contour in the class of piecewise meromorphic functions multiple of a given divisor. All the results are known and belong to the author (15-17), except for the existence theorems and properties of basic functionals and also properties of a θ-function. The solution of the problem in a 'special case' has been announced by the author but not published (15). Similar problems and some applications are considered in (1, 2, 12). The main results of the paper were obtained by the author during his collaboration with Professor G. S. Litvinchuk, and this paper is devoted to his cherished memory.
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