Geodesic
Multiplicative functions and Prym differentials on variable torus
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 1, pp. 74-90

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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.
Keywords: multiplicative functions and Prym differentials on compact Riemann surface, Teichmueller space, abelian differentials on torus, character group. 
@article{VNGU_2012_12_1_a4,
     author = {T. S. Krepitsina and V. V. Chueshev},
     title = {Multiplicative functions and {Prym} differentials on variable torus},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {74--90},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2012_12_1_a4/}
}
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T. S. Krepitsina; V. V. Chueshev. Multiplicative functions and Prym differentials on variable torus. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 1, pp. 74-90. http://geodesic.mathdoc.fr/item/VNGU_2012_12_1_a4/