MULTIPLICATIVE FUNCTIONS AND PRYM DIFFERENTIALS ON VARIABLE TORUS
In this article started construction general theory of multiplicative functions and Prym differentials on variable torus. The Abel's theorem are proved. Dimensions spaces of holomorphic multiplicative functions and Prym differentials on torus are found. New properties for spaces of meromorphic Prym differentials on variable torus are obtained. For two important factor spaces such differentials constructed basics. Moreover, dimension the ﬁrst holomorphic de Rham cohomology group of Prym differentials for characters on torus are obtained.