| Project/Area Number |
18K13401
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Ehime University (2020-2023)
Institute of Physical and Chemical Research (2018-2019) |
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Principal Investigator |
Ishikawa Isao 愛媛大学, データサイエンスセンター, 准教授 (80804236)
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | 捻れ三重積p進L関数 / 保形表現 / p進L関数 / 捻れ3重積 / L関数の特殊値 / 保型表現 / 岩澤理論 / 数論幾何学 / 保型形式 |
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| Outline of Final Research Achievements |
In this research, we reexamined the consistency of local factors between the Galois and automorphic sides for Asai representations on GL_2. We performed explicit calculations of the local factors associated with Asai representations in the case of GL_2, proving the consistency between the automorphic and Galois sides. These results were submitted to a journal and accepted. We also attempted to generalize these findings to GL_n cases.
Additionally, despite the impact of the COVID-19 pandemic, we developed new strategies for the generalization of the construction of p-adic L-functions, considering the integrality and the construction of the Hida p-adic family in the context of automorphic representations on unitary groups using the Ichino-Ikeda conjecture. We aimed to reconstruct existing construction methods by utilizing structures inherent in general algebraic groups, independent of the specific form of the GL_2 group.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は、GL_2おけるAsai表現の局所因子の一致性を局所的な手法で証明し、さらにGL_nまで考察を広げることで数論と保型表現論における理論的進展をもたらした。また、捻れ3重積L関数の一般化により、L関数と保型形式の理論を発展させた。さらに、p進L関数の構成法の一般化により、p進解析に新たな技術が提供することができる。
本研究は、p進L関数や保型表現の分野を通した学術的発展を促進し、新しい理論や手法の確立は、数学コミュニティの活性化に寄与するものである。
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