Twisted Cycles and Twisted Period Relations for Lauricella's Hypergeometric Function Fc

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