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We show that the cohomology intersection number of a twisted Gauss-Manin connection with regularization condition is a rational function.
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K.Ohara, Y.Sugiki, N.Takayama, Quadratic relations for generalized hypergeometric functions F p − 1 p {}_{p}F_{p-1} , Funkcialaj Ekvacioj 46
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S.J.Matsubara-Heo, N.Takayama, GKZ hypergeometric system (manual for mt_gkz.rr), http://www.math.kobe-u.ac.jp/OpenXM/Math/intersection2/Prog/mt_gkz-en.pdf
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Y.Goto, K.Matsumoto, Pfaffian of Appell’s hypergeometric system F 4 F_{4} in terms of the intersection form of twisted cohomology groups, Nagoya Mathematical Journal (2015), 61–94
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T.Hibi, K.Nishiyama, N.Takayama, Pfaffian systems of A A -hypergeometric equations I: Bases of twisted cohomology groups, Adv. Math. 306
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Y.Goto, , K.Matsumoto, Pfaffian equations and contiguity relations of the hypergeometric function of type ( k + 1 , k + n + 2 ) (k+1,k+n+2) and Their Applications, Funkcialaj Ekvacioj 61
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S.J.Matsubara-Heo, N.Takayama, Algorithms for Pfaffian Systems and Cohomology Intersection Numbers of Hypergeometric Integrals, Mathematical software—ICMS 2020. Lecture Notes in Computer Science, 12097. Springer, 73–84, (Errata at http://www.math.kobe-u.ac.jp/OpenXM/Math/intersection2
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