2013 Fiscal Year Final Research Report
Research on arithmetic properties of multiple Dirichlet series
| Project/Area Number |
23540022
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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 | Tokyo Metropolitan University |
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Principal Investigator |
TSUMURA Hirofumi 首都大学東京, 大学院理工学研究科, 教授 (20310419)
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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)
KOMORI Yasushi 立教大学, 理学部数学科, 准教授 (80343200)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 代数学 / 整数論 / ゼータ関数 |
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| Research Abstract |
We study analytic properties of the multiple Dirichlet series from the various viewpoints. In particular, we obtain some value-relations and functional relations for them, and consider their applications to number theory. Concretely we study Witten's zeta-functions associated with the root systems and certain Eisenstein type series as a joint work with K. Matsumoto (Nagoya University) and Y. Komori (Rikkyo University). Our research is being completed as a fruitful theory. As for double zeta-functions, we obtain a new type of the mean value theorem. We greatly expect its application to number theory.
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