TWISTED CYCLES AND TWISTED PERIOD RELATIONS FOR LAURICELLA'S HYPERGEOMETRIC FUNCTION FC

Abstract

We study Lauricella's hypergeometric function FC by using twisted (co)homology groups. We construct twisted cycles with respect to an Euler-type integral representation of FC. These cycles correspond to 2m linearly independent solutions to the system of differential equations annihilating FC. Using intersection forms of twisted (co)homology groups, we obtain twisted period relations which give quadratic relations for Lauricella's FC.