Pfaffian Systems of Confluent Hypergeometric Functions of Two Variables

• Material Type: 博士論文
• Title: Pfaffian Systems of Confluent Hypergeometric Functions of Two Variables
• Author/Editor: 向井, 重雄
• Author Heading: 向井, 重雄
• Publication, Distribution, etc.: Hokkaido University
• Publication Date: 2021-09-24
• Publication Date (W3CDTF): 2021-09-24
• Alternative Title: 2変数合流型超幾何関数のパフィアン系
• Contributor: 松本, 圭司; 岩﨑, 克則; 齋藤, 睦
• Degree grantor/type: 北海道大学
• Date Granted: 2021-09-24
• Date Granted (W3CDTF): 2021-09-24
• Dissertation Number: 甲第14641号
• Degree Type: 博士(理学)
• Conferring No. (Dissertation): 甲第14641号
• Text Language Code: eng
• Alias of Author: Mukai, Shigeo
• NDC: 400
• Target Audience: 一般
• Note (General): We study Pfaffian systems of confluent hypergeometric functions of two variables with rank three and rank four. This paper is composed of two parts. In part I, we study Pfaffian systems of two variables with rank three by using rational twisted cohomology groups associated with Euler type integrals of these functions. We give bases of the cohomology groups, whose intersection matrices depend only on parameters. Each connection matrix of our Pfaffian systems admits a decomposition into five parts, each of which is the product of a constant matrix and a rational 1-form on the space of variables. In part II, we consider confluences of Euler type integrals expressing solutions to Appell's F2 system of hypergeometric differential equations, and study systems of confluent hypergeometric differential equations of rank four of two variables. Our consideration is based on a confluence transforming the abelian group (Cx)2 to the Jordan group of size two. For each system obtained by our study, we give its Pfaffian system with a connection matrix admitting a decomposition into four or five parts, each of which is the product of a matrix depending only on parameters and a rational 1-form in two variables. We classify these Pfaffian systems under an equivalence relation. Any system obtained by our study is equivalent to one of Humbert's Ψ1 system, Humbert's Ξ1 system, and the system satisfied by the product of two Kummer's confluent hypergeometric functions.; (主査) 教授 松本 圭司, 教授 岩﨑 克則, 教授 齋藤 睦; 理学院（数学専攻）
• DOI: 10.14943/doctoral.k14641; https://doi.org/10.14943/doctoral.k14641
• Persistent ID (NDL): info:ndljp/pid/11977040; https://dl.ndl.go.jp/pid/11977040
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• Collection (particular): 国立国会図書館デジタルコレクション > デジタル化資料 > 博士論文; https://dl.ndl.go.jp/collections/A00014
• Acquisition Basis: 博士論文（自動収集）
• Date Accepted (W3CDTF): 2022-01-10T16:22:37+09:00
• Format (IMT): PDF
• Access Restrictions: 国立国会図書館内限定公開
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• Periodical Title (URI): http://dx.doi.org/10.14943/doctoral.k14641; http://hdl.handle.net/2115/83469
• Is Referenced By (URI): http://hdl.handle.net/2115/83468
• Data Provider (Database): 国立国会図書館 : 国立国会図書館デジタルコレクション; https://dl.ndl.go.jp