Newform Theory for automorphic forms and its applications to Iwasawa Theory
| Project/Area Number |
15K04783
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nara Women's University |
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Principal Investigator |
Okazaki Takeo 奈良女子大学, 自然科学系, 准教授 (80437334)
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| Project Period (FY) |
2015-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 保型形式 / 保型表現 / 算術離散群 / 新形式理論 / ラングランズ対応 / Siegel 保型形式 / ゼータ関数 / Modular forms / L-function / New form / Modular variety / NewForm |
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| Outline of Final Research Achievements |
I tried to construct a newform theory for irreducible admissible representations of GSp(4), that is Siegel modular forms of degree 2 in the classical sense. I have completed to the construction for the generic case, which is a generalization of Roberts and Schmidt for PGSp(4), and for the Saito-Kurokawa lifts, a non-generic case.
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| Academic Significance and Societal Importance of the Research Achievements |
楕円保型形式のNewform理論が, 1970年代に構築され様々な応用があることからSiegel保型形式でもまた重要である.様々な研究分野からも重要視される次数2の正則Siegel保型形式は, 大域Whittaker模型を持たず, 大域Bessel模型でNewform理論を構築することが望まれる. 今回局所Whittaker 模型をもつcaseと大域Bessel模型を持つ1caseである斎藤-黒川リフトでNewform理論を構築した. この結果により一般に, 今回新たに発見した擬-非分裂型paramodular群によりNewform理論が構築されることが期待される.
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Report
(6 results)
Research Products
(2 results)
