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 $T$.
"Euler and Laplace integral representations of GKZ hypergeometric functions II." Proc. Japan Acad. Ser. A Math. Sci. 96 (9) 79 - 82, November 2020. https://doi.org/10.3792/pjaa.96.015