Twisted cycles and twisted period relations for Lauricella's hypergeometric function F_C

TL;DR

This paper investigates Lauricella's hypergeometric function F_C through twisted homology and cohomology, constructing cycles and deriving quadratic relations that deepen understanding of its solutions and differential equations.

Contribution

It introduces a novel approach using twisted (co)homology to construct solutions and derive period relations for F_C, expanding the theoretical framework.

Findings

Constructed twisted cycles corresponding to solutions of F_C

Derived twisted period relations leading to quadratic relations

Connected intersection forms with differential equations

Abstract

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.