2013 Fiscal Year Final Research Report
Studies on various multiple zeta-functions associated with root systems
| Project/Area Number |
22540045
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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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| Co-Investigator(Renkei-kenkyūsha) |
MATSUMOTO Kohji 名古屋大学, 大学院多元数理科学研究科, 教授 (60192754)
TSUMURA Hirofumi 首都大学東京, 大学院理工学研究科, 教授 (20310419)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 多重ゼータ関数 |
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| Research Abstract |
Both partition functions in quantum gauge theories and zeta-functions in mathematics, which play fundamental and important roles in each area, happen to coincide in some cases. Among them are the Witten zeta-functions. Special values of these zeta-functions at positive integers are the main objects and should be studied from various viewpoints. For this problem, we established a unified way to treat these values via their generating functions. We also obtained new functional relations and formulas for related zeta-functions and hypergeometric functions from the viewpoint of root systems.
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