INTERSECTION NUMBERS AND TWISTED PERIOD RELATIONS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION _<m+1>F_m

Abstract

We consider the generalized hypergeometric function _<m+1>E_m and the differential equation _<m+1>E_m that it satisfies. We use the twisted (co)homology groups associated with an Euler-type integral representation. We evaluate the intersection numbers of the twisted cocycles that are defined as the mth exterior productsof logarithmic 1-forms. We also provide the twisted cycles corresponding to the local solutions to _<m+1>E_m around the origin, and we evaluate their intersection numbers. The intersection numbers of the twisted (co)cycles lead to the twisted period relations between two fundamental systems of solutions to _<m+1>E_m