The structure of bivariate rational hypergeometric functions

E. CATTANI, A. DICKENSTEIN, F. RODRIGUEZ VILLEGAS

INTERNATIONAL MATHEMATICS RESEARCH NOTICES

OXFORD UNIV PRESS

Año: 2010

1073-7928

We describe the structure of all codimension-two lattice congurationsA which admit a stable rational A-hypergeometric function, that is arational function F all whose partial derivatives are non zero, and which is a solutionof the A-hypergeometric system of partial dierential equations denedby Gel'fand, Kapranov and Zelevinsky. We show, moreover, that all stablerational A-hypergeometric functions may be described by toric residues andapply our results to study the rationality of bivariate series whose coeffcientsare quotients of factorials of linear forms.