| Project/Area Number |
18K03221
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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 | Keio University |
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Principal Investigator |
Yamamoto Shuji 慶應義塾大学, 理工学研究科(矢上), 特任准教授 (20635370)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 多重ゼータ値 / 多重ゼータ関数 / 川島関数 |
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| Outline of Final Research Achievements |
Multiple zeta values, the values of the multiple zeta function evaluated at positive integer points, are intensively studied from various viewpoints. On the other hand, it is non-trivial to define the values at (not necessarily positive) integer points, because of the singularity of the function. In this research, we explored a new approach to the multiple zeta values of non-positive indices, mainly through the studies of certain special functions, called the Kawashima functions. Then we obtained a new integral representation of the Kawashima function, the complex analytic extension with respect to the index and relations with the multiple zeta functions of Hurwitz type. Moreover, we also showed an extension of the Kaneko-Zagier conjecture on finite and symmetric multiple zeta values to non-positive indices.
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| Academic Significance and Societal Importance of the Research Achievements |
学術的意義として，まず川島関数についてこの研究で明らかになった新たな性質・公式はそれ自身として興味深いものであり，今後の研究にも広がる可能性を持っている．また金子ザギエ予想はこの分野の重要な未解決問題の一つであるが，それが非正指数へ自然に拡張されたことは，多重ゼータ値の文脈において「正から非正への拡張」という問いが生産的な方向であり得ることを示唆している．
一方，この研究の社会的意義を評価するのは困難であるが，日本人の名を冠する川島関数の研究を日本において継続・発展させることについて文化的意義を見出すことはできよう．
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