Intersection numbers and twisted period relations for the generalized hypergeometric function ${}_{m+1}{F}_m$

Abstract

We study the generalized hypergeometric function ${}_{m+1}{F}_m$ and the differential equation ${}_{m+1}{E}_m$ satisfied by it. We use the twisted (co)homology groups associated with an integral representation of Euler type. We evaluate the intersection numbers of some twisted cocycles which are defined as $m$-th exterior products of logarithmic $1$-forms. We also give twisted cycles corresponding to the series solutions to ${}_{m+1}{E}_m$, and evaluate the intersection numbers of them. These intersection numbers of the twisted (co)cycles lead twisted period relations which give relations for two fundamental systems of solutions to ${}_{m+1}{E}_m$.

13 pages

Cited by in corpus (1)

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