TY  - INPR
A1  - Sadykov, Timour
T1  - Hypergeometric systems of differential equations and amoebas of rational functions
N2  - We study the approach to the theory of hypergeometric functions in several variables via a generalization of the Horn system of differential equations. A formula for the dimension of its solution space is given. Using this formula we construct an explicit basis in the space of holomorphic solutions to the generalized Horn system under some assumptions on its parameters. These results are applied to the problem of describing the complement of the amoeba of a rational function, which was posed in [12].
T3  - Preprint - (1999) 33 
Y1  - 2008
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2357
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-25665
ER  -