Euler and Laplace integral representations of GKZ hypergeometric functions II

Abstract

We establish the intersection theory of the rapid decay homology group and formulate the twisted period relation in this setting. We claim that there is a standard method of constructing a basis of the rapid decay homology group which can be related to GKZ hypergeometric series. This can be carried out with the aid of a convergent regular triangulation $T$. When $T$ is unimodular, we can obtain a closed formula of the homology intersection number. Finally, we obtain a Laurent series expansion formula of the cohomology intersection number in terms of the combinatorics of $T$.