Geodesic
Residues and Elementary Prym Differentials on the Compact Riemann Surface
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 2, pp. 99-118

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The paper are obtained new results on the theory of multiplicative functions and Prym differentials on a variable compact Riemann surfaces of genus $g>1$. For the first time full sum residues theorems are obtained for Prym differentials for every integer order. As a corollary reciprocity laws and existence theorems for Prym differentials with given poles and residues are proven. All kinds of elementary Prym differentials, which holomorphically depend on modules of surfaces and characters are constructed. Analogues of Appell's decomposition formula for functions with characters are proven.
Keywords: Compact Riemann surfaces, Prym differentials, characters.
Mots-clés : Teichmueller spaces 
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     author = {T. A. Pushkareva},
     title = {Residues and {Elementary} {Prym} {Differentials} on the {Compact} {Riemann} {Surface}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {99--118},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2013_13_2_a9/}
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T. A. Pushkareva. Residues and Elementary Prym Differentials on the Compact Riemann Surface. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 2, pp. 99-118. http://geodesic.mathdoc.fr/item/VNGU_2013_13_2_a9/