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Pfaffian Systems of Confluent Hypergeometric Functions of Two Variables

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Title: Pfaffian Systems of Confluent Hypergeometric Functions of Two Variables
Other Titles: 2変数合流型超幾何関数のパフィアン系
Authors: 向井, 重雄1 Browse this author
Authors(alt): Mukai, Shigeo1
Issue Date: 24-Sep-2021
Publisher: Hokkaido University
Abstract: 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.
Conffering University: 北海道大学
Degree Report Number: 甲第14641号
Degree Level: 博士
Degree Discipline: 理学
Examination Committee Members: (主査) 教授 松本 圭司, 教授 岩﨑 克則, 教授 齋藤 睦
Degree Affiliation: 理学院(数学専攻)
Type: theses (doctoral)
Appears in Collections:課程博士 (Doctorate by way of Advanced Course) > 理学院(Graduate School of Science)
学位論文 (Theses) > 博士 (理学)

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