an:04188193
Zbl 0721.33006
Gel'fand, I. M.; Zelevinskij, A. V.; Kapranov, M. M.
Hypergeometric functions and toric varieties
EN
Funct. Anal. Appl. 23, No. 2, 94-106 (1989); translation from Funkts. Anal. Prilozh. 23, No. 2, 12-26 (1989); correction Funct. Anal. Appl. 27, No. 4, 295 (1993); translation from Funkts. Anal. Prilozh. 27, No. 4, 91 (1993).
00181689
1989
j
33C70 34A25 14Q99
Newton polyhedron
The paper studies the holonomy systems of linear differential equations connected with linear representations of complex tori. The characteristic manifold, the characteristic cycle of the system and, in particular, the number of independent solutions in a neighbourhood of a given point are expressed in terms of the volume of the corresponding Newton polyhedron. The basis of the space of solutions is expressed explicitly using the series of hypergeometric type. The paper contains also a number of examples which include many classical hypergeometric functions of one or several variables.
V.M??ller