Intersection numbers and twisted period relations for the generalized hypergeometric function _m+1 F_m

2014/06/29 by Yoshiaki Gotō, Goto, Yoshiaki
Computer Science · Mathematics · Physics and Astronomy · #33C20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1406.7464

openalex publication_date 2014/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the generalized hypergeometric function _m+1 F_m and the differential equation _m+1E_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+1E_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+1E_m.

Related

• Twisted period relations for Lauricella's hypergeometric function F_A
• Contiguity relations of Lauricella's F_D revisited
• The monodromy representation and twisted period relations for Appell's hypergeometric function F₄
• Intersection numbers of twisted cycles and cocycles for degenerate arrangements
• The Elliptic Hypergeometric Functions Associated to the Configuration Space of Points on an Elliptic Curve I : Twisted Cycles