| Project/Area Number |
25247001
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
若槻 聡 金沢大学, 数物科学系, 准教授 (10432121)
佐藤 文広 津田塾大学, 付置研究所, 研究員 (20120884)
北山 秀隆 和歌山大学, 教育学部, 准教授 (20622567)
桂田 英典 室蘭工業大学, 工学研究科, 教授 (80133792)
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| Co-Investigator(Renkei-kenkyūsha) |
Hayashida Shuichi 上越教育大学, 大学院学校教育研究科, 准教授 (80597766)
Watanabe Takao 大阪大学, 大学院理学研究科, 教授 (30201198)
Moriyama Tomonori 大阪大学, 大学院理学研究科, 准教授 (80384171)
Ochiai Tadashi 大阪大学, 大学院理学研究科, 准教授 (90372606)
Ikeda Tamotsu 京都大学, 大学院理学研究科, 教授 (20211716)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥25,090,000 (Direct Cost: ¥19,300,000、Indirect Cost: ¥5,790,000)
Fiscal Year 2017: ¥5,980,000 (Direct Cost: ¥4,600,000、Indirect Cost: ¥1,380,000)
Fiscal Year 2016: ¥6,500,000 (Direct Cost: ¥5,000,000、Indirect Cost: ¥1,500,000)
Fiscal Year 2015: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2014: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2013: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
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| Keywords | ジーゲル保型形式 / ヤコービ保型形式 / テータ関数 / ゲーゲンバウア関数 / 微分作用素 / ホロノミー系 / ゼータ関数 / コンパクト実形 / 概均質ベクトル空間 / ヤコービ形式 / 跡公式 / 特殊関数論 / ２次形式 / 保型的微分作用素 / 保型形式の合同 / 超特異アーベル多様体 / ４元数的エルミート形式 / L 関数 / アーベル多様体 / 整数論 / 保型形式 / 代数学 / Ｌ関数 / 特殊値 / 特殊関数 / リフティング / 種の理論 |
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| Outline of Final Research Achievements |
In study of the number theory, functions called automorphic forms are important objects which describe various arithmetic properties. We gave many results on these in this project. A theory of automorphic differential operators includes the classical theory of special functions such as Gegenbauer functions, and in our study, we gave three different complete constructions for these operators, which can be regarded as final results. We also gave explicit solutions of associated system of differential equations. We gave conjectures on comparison of
automorphic forms belonging to different domains, and structure theorems of automorphic forms by using constructive methods including automorphic differential operators. Some dimension formulas of automorphic forms and trace formulas of arithmetically important Hecke operators were given, and we clarified their relations to arithmetic invariants in some algebraic geometry over finite fields.
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