2013 Fiscal Year Final Research Report
Explicit study of arithmetic structures of automorphic forms of several variables and trace formulas
| Project/Area Number |
21244001
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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) |
WAKATSUKI Satoshi 金沢大学, 数物科学系, 准教授 (10432121)
KATSURADA Hidenori 室蘭工業大学, 工学研究科, 教授 (80133792)
SATO Fumihiro 立教大学, 理学部, 教授 (20120884)
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| Co-Investigator(Renkei-kenkyūsha) |
IKEDA Tamotsu 京都大学, 理学研究科, 教授 (20211716)
ODA Takayuki 東京大学, 数理科学研究科, 教授 (10109415)
SAITO Kyoji 東京大学, 数物連携宇宙研究機構, 特任教授 (20012445)
NAGAOKA Shoyu 近畿大学, 理工学部, 教授 (20164402)
OCHIAI Tadashi 大阪大学, 理学研究科, 准教授 (90372606)
MORIYAMA Tomonori 大阪大学, 理学研究科, 准教授 (80384171)
WATANABE Takao 大阪大学, 理学研究科, 教授 (30201198)
SUGANO Takashi 金沢大学, 数物科学系, 教授 (30183841)
BANNAI Eiichi 九州大学, 名誉教授 (10011652)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 整数論 / 保型形式 / 跡公式 / ゼータ関数 / リフティング / 合同 / 微分作用素 / 特殊関数論 |
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| Research Abstract |
In study of the number theory, functions called automorphic forms and their L functions are important objects which describe various arithmetic properties. We gave many results on these in this project. Among others, we gave structure theorems and dimension formulas of some automorphic forms, and based on these, we proposed three precise new conjectures which claim that several spaces of automorphic forms whose definitions and origins are completely different have essentially the same arithmetical structures. We also gave three new lifting conjectures which claim that some parts of such spaces of automorphic forms come from easier spaces. Using the theory we exploited on special functions associated with differential operators, we newly calculated explicit values of some L functions, and gave a proof of Zagier's conjecture in 1976 and some number-theoretic applications. Together with other newly obtained results, these contribute to the development of the theory of automorphic forms.
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[Presentation] lift (2)2011
Author(s)
伊吹山知義、Saito Kurokawa
Organizer
第19回整数論サマースクール
Place of Presentation
富士箱根ランド・スコーレプラザホテル
Year and Date
2011-09-06
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