2024-03-28T22:07:38Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/553172022-11-17T02:08:08Zhdl_2115_20136hdl_2115_54835hdl_2115_20124hdl_2115_54823hdl_2115_54822Geometric study of Lauricella's hypergeometric function FCLauricellaの超幾何関数 FCに関する幾何学的研究後藤, 良彰Goto, Yoshiaki松本, 圭司齋藤, 睦山下, 博澁川, 陽一吉永, 正彦open accessHypergeometric functionLauricella’s FCTwisted (co)homology groupsTwisted cyclesTwisted period relationsMonodromy representations400We 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.(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 正彦理学院(数学専攻)Hokkaido University2014-032014-03-25engdoctoral thesisVoRhttps://doi.org/10.14943/doctoral.k11364http://hdl.handle.net/2115/5531710.14943/doctoral.k11364http://hdl.handle.net/2115/5530260p.甲第11364号博士(理学)2014-03-2510101北海道大学Hokkaido Universityhttps://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/55317/1/Yoshiaki_Goto.pdfapplication/pdf361.97 KB2014-03-25