2022 Fiscal Year Final Research Report
Comprehensive study of multiple zeta functions and their application to quantum integrable systems
| Project/Area Number |
17K05185
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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 | Rikkyo University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2023-03-31
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| Keywords | 多重ゼータ関数 / ルート系 |
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| Outline of Final Research Achievements |
Multiple zeta functions associated with root systems are studied by various methods for their special values and relations among them, and in particular, a description in terms of the generating functions is given as a unified viewpoint. Using this description, we can obtain a very large class of relations associated with each root system and its subroot systems. In addition, the theory has been developed by reexamining, simplifying, and improving the proofs of a large number of results obtained through previous research, and by incorporating new arguments and examples, we will publish a book that is easy to read even for beginners. I believe that this book will make a significant contribution to the development of the theory of zeta functions of root systems.
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| Free Research Field |
代数学
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| Academic Significance and Societal Importance of the Research Achievements |
近年, 数論で最も重要な量のひとつであるゼータ関数と量子論で最も重要な量のひとつである分配関数とが結びついているという発見から新たな研究が生まれ、大きく発展し始めている. 本研究によって, 量子論やリー群を軸として広がりを見せている様々な多重ゼータ関数について, 分野を超えた広い枠組みで捉えることができ， 特殊値や関数関係式を通して多重ゼータ値の数論的理解や量子可積分系の基礎的な量の計算に貢献できたと考えている.
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