Geodesic
Prym differentials and Teichm\"uller spaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 686-691

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In this article we study multiplicative meromorphic functions and differentials on Riemann surfaces of finite type. We proved an analogue of P. Appell's formula on decomposition of multiplicative functions with poles of arbitrary multiplicity into a sum of elementary Prym integrals. We construct explicit bases for some important factor spaces and prove a theorem on a fiber isomorphism of vector bundles and $n!$-sheeted mappings over Teichmüller spaces. This theorem gives an important relation between spaces of Prym differentials on a compact Riemann surfaces and on a Riemann surfaces of finite type.
Keywords: Teichmüller spaces for Riemann surfaces of finite type, Prym differentials, vector bundles, group of characters, Jacobi manifolds. 
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     author = {Alexander V. Chueshev and Victor V. Chueshev},
     title = {Prym differentials and {Teichm\"uller} spaces},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {686--691},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a3/}
}
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Alexander V. Chueshev; Victor V. Chueshev. Prym differentials and Teichm\"uller spaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 686-691. http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a3/