arXiv 0907.07902009-07-17math.AGmath.COmath.NT

The structure of bivariate rational hypergeometric functions

Eduardo Cattani, Alicia Dickenstein, Fernando Rodriguez Villegas

备注：: 25 pages, 1 figure. Minor changes

英文摘要：

We describe the structure of all codimension-two lattice configurations $A$ which admit a stable rational $A$-hypergeometric function, that is a rational function $F$ all whose partial derivatives are non zero, 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 whose coefficients are quotients of factorials of linear forms.

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