INTERSECTION NUMBERS AND TWISTED PERIOD RELATIONS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION F-m+1(m)

摘要

We consider the generalized hypergeometric function F-m+1(m) and the differential equation E-m+1(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 products of logarithmic 1-forms. We also provide the twisted cycles corresponding to the local solutions to E-m+1(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 E-m+1(m).