# The structure of bivariate rational hypergeometric functions - Mathematics > Algebraic Geometry

The structure of bivariate rational hypergeometric functions - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: We describe the structure of all codimension-two lattice configurations $A$which admit a stable rational $A$-hypergeometric function, that is a rationalfunction $F$ all whose partial derivatives are non zero, and which is asolution of the $A$-hypergeometric system of partial differential equationsdefined by Gel-fand, Kapranov and Zelevinsky. We show, moreover, that allstable rational $A$-hypergeometric functions may be described by toric residuesand apply our results to study the rationality of bivariate series whosecoefficients are quotients of factorials of linear forms.

Author: ** Eduardo Cattani, Alicia Dickenstein, Fernando Rodriguez Villegas**

Source: https://arxiv.org/