Explicit and constructive research of automorphic forms of several variables

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K05076
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Tokyo University of Science
• Principal Investigator: AOKI Hiroki 東京理科大学, 理工学部数学科, 准教授 (10333189)
• Research Collaborator: HAYASHIDA Shuichi
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 保型形式 / ヤコビ形式 / ヒルベルト保型形式

Outline of Final Research Achievements

Although automorphic forms of several variables are important research subjects, their research is generally more difficult than in the case of one variable. This research work was conducted with the purpose of obtaining more knowledge about automorphic forms of several variables by the researcher's own research method using Jacobi forms. The results obtained during this research period are as follows:
`Struture theorem of Jacobi forms of real weights and indces' `Determination of the structures of mixed weight Hilbert modular forms' `A construction of Maass lift of weak Jacobi forms'.

Free Research Field

保型形式

Academic Significance and Societal Importance of the Research Achievements

多変数の保型形式は、整数論のみならず幾何学においても重要な研究対象であり、さらに近年では素粒子論においても使われはじめている。本研究では、いくつかの多変数の保型形式について、それはどのくらいあるのか、また具体的にどのような形をしているのかという問いに回答を与えた。これは保型形式そのものに関する疑問を解決したにとどまらず、上述の諸分野の研究に進展をもたらすものである。