The monodromy representation and twisted period relations for Appell’s hypergeometric function F4

Abstract

We consider the system ${\mathcal{F}}_4(a,b,c)$ of differential equations annihilating Appell’s hypergeometric series $F_4(a,b,c;x)$. We find the integral representations for four linearly independent solutions expressed by the hypergeometric series $F_4$. By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation of ${\mathcal{F}}_4(a,b,c)$ and the twisted period relations for the fundamental systems of solutions of ${\mathcal{F}}_4$.