A Criterion for Finite Hypergeometric Reductions of Lauricella's $F_C$ with Arguments Related by Cube Roots of Unity

Ryunosuke Nakano

We consider the germ at the origin of Lauricella's function $F_C^{(3)}(a,b;c_0,c_1,c_2;\kappa ,\omega \kappa ,{\omega }^2\kappa )$, where $\omega =\exp (2\pi \sqrt{-1}/3)$. We assume that $a,b,c_0,c_1,c_2$ avoid nonpositiv…