Geometric study of Lauricella's hypergeometric function FC

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Bibliographic Information

Title
Geometric study of Lauricella's hypergeometric function FC
Other Title
  • Lauricellaの超幾何関数 FCに関する幾何学的研究
Author
Goto, Yoshiaki
Alias Name
  • 後藤, 良彰
University
Hokkaido University
Types of degree
博士(理学)
Grant ID
甲第11364号
Degree year
2014-03-25

Description

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.

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