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The monodromy representation and twisted period relations for Appell’s hypergeometric function F 4

Part of: Deformations of analytic structures Singularities

Published online by Cambridge University Press:  11 January 2016

Yoshiaki Goto  and
Keiji Matsumoto
Yoshiaki Goto
Affiliation:
Department of Mathematics, Graduate School of Science, Kobe University, Kobe 657-8501, Japan, y-goto@math.kobe-u.ac.jp
Keiji Matsumoto
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan, matsu@math.sci.hokudai.ac.jp
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Abstract

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We consider the system F4 (a, b, c) of differential equations annihilating Appell's hypergeometric series F4(a,b,c;x). We find the integral representations for four linearly independent solutions expressed by the hypergeometric series F4 . By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation of F4(a, b, c) and the twisted period relations for the fundamental systems of solutions of F 4.

MSC classification

Secondary: 33C65: Appell, Horn and Lauricella functions 32G20: Period matrices, variation of Hodge structure; degenerations 32S40: Monodromy; relations with differential equations and $D$-modules

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 217 , March 2015 , pp. 61 - 94
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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