Nonequivalent coverings of Riemann surfaces with a prescribed ramification type (Q1079698)

Continuing his investigation [Dokl. Akad. Nauk SSSR 239, 269-271 (1978; Zbl 0395.30034); ibid. 244, 529-532 (1979; Zbl 0416.30038)], the author gives complete proofs for theorems that he announced in a previous paper [ibid. 261, 537-542 (1981; Zbl 0506.30031)] and gives in terms of irreducible representations of symmetric groups a complete solution of the A. Hurwitz problem on the number of topologically nonequivalent coverings of a compact Riemann surface of genus p with a given type of ramification. In these same terms, he gives for every p necessary and sufficient conditions for the existence of such coverings and shows that asymptotically almost all coverings with a fixed type of ramification have a trivial group of transformations of the covering. See also a paper by \textit{H. Röhrl} [Trans. Am. Math. Soc. 107, 320-346 (1963; Zbl 0115.067)].