340 research outputs found

    Intersection numbers and twisted period relations for the generalized hypergeometric function m+1Fm{}_{m+1} F_m

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    We study the generalized hypergeometric function m+1Fm{}_{m+1} F_m and the differential equation m+1Em{}_{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 mm-th exterior products of logarithmic 11-forms. We also give twisted cycles corresponding to the series solutions to m+1Em{}_{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+1Em{}_{m+1}E_m.Comment: 13 page
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