Research of automorphic forms of several variables by Jacobi forms

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03429
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11010:Algebra-related
• Research Institution: Tokyo University of Science
• Principal Investigator: AOKI Hiroki 東京理科大学, 創域理工学部数理科学科, 教授 (10333189)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 保型形式 / ヤコビ形式 / 無限積 / 整数論 / モジュラー群

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 using Jacobi forms. Two main research results during the period were ``new evaluation of the vanishing order of the space of Jacobi forms'' and ``characterization of Jacobi forms constructed by infinite products.'' These two results are closely related to what we wanted to clarify at the time of application. Although we were not able to reach a final resolution within the period due to the effects of the COVID pandemic, we feel that we are getting very close to our goal.

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「ヤコビ形式のなす空間の消滅次数についての新たな評価」「無限積で構成されるヤコビ形式の特徴づけ」という２つの成果を得た。これは保型形式そのものに関する新しい結果であると同時に、上述の諸分野の研究に進展をもたらすものである。