| Project/Area Number |
17K14174
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyushu University (2018-2021)
Tokyo Denki University (2017) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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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: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 岩澤理論 / L関数 / 保型表現論 / p進L関数 / 数論 / 保型表現 |
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| Outline of Final Research Achievements |
We studied about period integrals for Asai representations and Rankin-Selberg products in an explicit manner. In particular, we constructed theta series on GSp(4) and we proved the Bessel period formulas and inner product formulas for these theta series, which give fundamental properties for modular Iwasawa theory for Asai representations. We also constructed p-adic Asai L-functions for GL(2) if the base field is a CM field. Furthermore, considering an analogue of Asai representations, we proved an explicit period integral formulas for Rankin-Selberg L-functions and we clarify a motivic background of Whittaker periods for GL(n) under standard conjectures such as an existence of motives corresponding automorphic representations.
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| Academic Significance and Societal Importance of the Research Achievements |
保型形式に関する周期積分の研究は, L関数の特殊値の研究において基本的である. 本研究により, 特殊値の数論的性質を調べるために周期積分の明示的な公式をいくつか得ることが出来た. これらはとくに浅井表現, Rankin-Selberg積のL関数に関する今後の岩澤理論的な研究にとっての基礎となっており, 今後のこの方面への研究の発展が期待される. また本研究の手法を他の表現, 代数群に対して適用することも興味深い.
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