Twisted period relations for Lauricella's hypergeometric function F_A

Abstract

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

13 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1308.5535

References in corpus (1)

• Groebner basis and singular locus of Lauricella's hypergeometric differential equations

Cited by in corpus (2)

• On the computation of intersection numbers for twisted cocycles
• Twisted cycles and twisted period relations for Lauricella's hypergeometric function F_C