| Project/Area Number |
18K03235
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
都築 正男 上智大学, 理工学部, 教授 (80296946)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Discontinued (Fiscal Year 2021)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 数論 / 保型形式 / 跡公式 / ヘッケ固有値 / 整数論 / 代数学 |
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| Outline of Final Research Achievements |
In this research, we studied Hecke eigenvalues of automorphic forms in number theory. Number theory is a field that studies various properties of natural numbers and primes, automorphic forms are mysterious functions which have high symmetry, and their Hecke eigenvalues are sequences of numbers which naturally arise from them. Hecke eigenvalues have very interesting number-theoretic properties, and a classical example of Hecke eigenvalues is Ramanujan's tau function. A major result of our research is that we have succeeded to prove various results on the distributions of their eigenvalues by considering natural families of automorphic forms.
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| Academic Significance and Societal Importance of the Research Achievements |
保型形式の族のヘッケ固有値の分布はプランシュレル測度や佐藤-テイト測度に従うことが予想されており、様々な場合に証明されている。ヘッケ固有値の漸近公式の一般化と精密化を推進することで、ヘッケ固有値の分布の性質をより統一的に明らかにすることが本研究の目的であった。実際、本研究の成果によって、その一般化と精密化の両方についてヘッケ固有値の漸近公式の研究を大きく進展させることができた。
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