36 citations · 71 across the 15 of their papers we have counts for
13 papers · 1 filter
Intersection numbers of twisted homology and cohomology groups associated to the Riemann-Wirtinger integral
Yoshiaki Goto
The Riemann-Wirtinger integral is an analogue of the hypergeometric integral, which is defined as an integral on a one-dimensional complex torus. We study the intersection forms on…
Homology and cohomology intersection numbers of GKZ systems
Yoshiaki Goto, Saiei-Jaeyeong Matsubara-Heo
We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twist…
Picard-Vessiot groups of Lauricella's hypergeometric systems and Calabi-Yau varieties arising integral representations
Yoshiaki Goto, Kenji Koike
We study the Zariski closure of the monodromy group of Lauricella's hypergeometric function . If the identity component acts irreducibly, then…
Intersection numbers of twisted cycles and cocycles for degenerate arrangements
Yoshiaki Goto
We study the intersection numbers defined on twisted homology or cohomology groups that are associated with hypergeometric integrals corresponding to degenerate hyperplane arrangem…
Irreducibility of the monodromy representation of Lauricella's
Yoshiaki Goto, Keiji Matsumoto
Let be the hypergeometric system of differential equations satisfied by Lauricella's hypergeometric series of variables. We show that the monodromy representation o…
Pfaffian equations and contiguity relations of the hypergeometric function of type and their applications
Yoshiaki Goto, Keiji Matsumoto
We study the structures of Pfaffian equations and contiguity relations of the hypergeometric function of type by using twisted cohomology groups and the intersection…
Pfaffian of Appell's hypergeometric system in terms of the intersection form of twisted cohomology groups
Yoshiaki Goto, Jyoichi Kaneko, Keiji Matsumoto
We study a Pfaffian of the system of differential equations annihilating Appell's hypergeometric series by twisted cohomology groups associated with integrals repres…
Contiguity relations of Lauricella's F_D revisited
Yoshiaki Goto
We study contiguity relations of Lauricella's hypergeometric function F_D, by using the twisted cohomology group and the intersection form. We derive contiguity relations from thos…
Intersection numbers and twisted period relations for the generalized hypergeometric function
Yoshiaki Goto
We study the generalized hypergeometric function and the differential equation satisfied by it. We use the twisted (co)homology groups associated with…
The monodromy representation of Lauricella's hypergeometric function F_C
Yoshiaki Goto
We study the monodromy representation of the system of differential equations annihilating Lauricella's hypergeometric function of variables. Our representation spa…
Twisted period relations for Lauricella's hypergeometric function F_A
Yoshiaki Goto
We study Lauricella's hypergeometric function of -variables and the system of differential equations annihilating , by using twisted (co)homology groups. We con…
The monodromy representation and twisted period relations for Appell's hypergeometric function F_4
Yoshiaki Goto, Keiji Matsumoto
We consider the system of differential equations annihilating Appell's hypergeometric series . We find the integral representations for four li…
Twisted cycles and twisted period relations for Lauricella's hypergeometric function F_C
Yoshiaki Goto
We study Lauricella's hypergeometric function F_C by using twisted (co)homology groups. We construct twisted cycles with respect to an Euler-type integral representation of F_C. Th…