Automorphic L-functions by using the generalized Maass relations

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400007
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Joetsu University of Education
• Principal Investigator: Hayashida Shuichi 上越教育大学, 大学院学校教育研究科, 准教授 (80597766)
• Co-Investigator(Renkei-kenkyūsha): AOKI Hiroki 東京理科大学, 理工学部, 准教授 (10333189)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: ランキン・セルバーグ型ディリクレ級数

Outline of Final Research Achievements

Siegel modular forms and Jacobi forms are modular forms of several variables. In this research some properties of Siegel modular forms and Jacobi forms were investigated. More precisely, the following results are obtained. The isomorphism between the space of Jacobi forms of matrix index of integral weight and of half-integral weight. The meromorphic continuation and functional equation for certain Rankin-Selberg type Dirichlet series (Kohnen-Skoruppa-Yamazaki type Dirichlet series). An explicit formula for a Kohnen-Skourppa-Yamazaki type Dirichlet series which is constructed from half-integral weight version of the Ikeda lift.

Free Research Field

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