Geodesic
On the solvability of the first Cousin problem for a~class of multivalued analytic functions
Izvestiya. Mathematics , Tome 35 (1990) no. 2, pp. 393-409

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The construction, by Maslov's method, of global asymptotics of solutions of differential equations on complex analytic manifolds leads to the first Cousin problem for a certain special class of multivalued analytic functions. This problem (having independent interest) is solved in the present paper. Bibliography: 9 titles. 
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     author = {B. Yu. Sternin and V. E. Shatalov},
     title = {On the solvability of the first {Cousin} problem for a~class of multivalued analytic functions},
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B. Yu. Sternin; V. E. Shatalov. On the solvability of the first Cousin problem for a~class of multivalued analytic functions. Izvestiya. Mathematics , Tome 35 (1990) no. 2, pp. 393-409. http://geodesic.mathdoc.fr/item/IM2_1990_35_2_a5/