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Geometric study of Lauricella's hypergeometric function FC

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Title: Geometric study of Lauricella's hypergeometric function FC
Other Titles: Lauricellaの超幾何関数 FCに関する幾何学的研究
Authors: 後藤, 良彰1 Browse this author
Authors(alt): Goto, Yoshiaki1
Keywords: Hypergeometric function
Lauricella’s FC
Twisted (co)homology groups
Twisted cycles
Twisted period relations
Monodromy representations
Issue Date: 25-Mar-2014
Publisher: Hokkaido University
Abstract: We study Lauricella’s hypergeometric function FC of m-variables by using twisted(co)homology groups. We construct twisted cycles with respect to an integralrepresentation of Euler type of FC. These cycles correspond to 2m linearly independentsolutions to the system EC of differential equations annihilating FC.Using intersection forms of twisted (co)homology groups, we obtain twisted periodrelations which give quadratic relations for Lauricella’s FC.We provide the monodromy representation of the system EC. We give generatorsof the fundamental group of the complement of the singular locus ofEC. We represent the circuit transformations along these generators by theintersection form on twisted homology groups.
Conffering University: 北海道大学
Degree Report Number: 甲第11364号
Degree Level: 博士
Degree Discipline: 理学
Examination Committee Members: (主査) 教授 松本 圭司, 教授 齋藤 睦, 教授 山下 博, 准教授 澁川 陽一, 准教授 吉永 正彦
Degree Affiliation: 理学院(数学専攻)
Type: theses (doctoral)
Appears in Collections:学位論文 (Theses) > 博士 (理学)
課程博士 (Doctorate by way of Advanced Course) > 理学院(Graduate School of Science)

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