Solving algebraic equations in terms of [formula omitted]-hypergeometric series

Abstract

The roots of the general equation of degree n satisfy an A -hypergeometric system of differential equations in the sense of Gel'fand, Kapranov and Zelevinsky. We construct the n distinct A -hypergeometric series solutions for each of the 2 n−1 triangulations of the Newton segment. This works over any field whose characteristic is relatively prime to the lengths of the segments in the triangulation.