The structure of bivariate rational hypergeometric functions

We describe the structure of all codimension-2 lattice configurations A which admit a stable rational A-hypergeometric function, that is a rational function F all the partial derivatives of which are nonzero, and which is a solution of the A-hypergeometric system of partial differential equations defined by Gel′ fand, Kapranov, and Zelevinsky. We show, moreover, that all stable rational A-hypergeometric functions may be described by toric residues and apply our results to study the rationality of bivariate series the coefficients of which are quotients of factorials of linear forms.Fil: Cattani, Eduardo. University Of Massachussets; Estados UnidosFil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Rodriguez Villegas, Fernando. University of Texas at Austin; Estados Unido