Research on analytic properties of multiple Dirichlet series and its application to number theory
| Project/Area Number |
20540020
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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 | Tokyo Metropolitan University |
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Principal Investigator |
TSUMURA Hirofumi Tokyo Metropolitan University, 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)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 数論 / 代数学 / 整数論 / ゼータ関数 |
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| Research Abstract |
The research representative established the foundation of the multiple zeta-functions associated with root systems through the joint work with Professors Kohji Matsumoto (Nagoya Univ.) and Yasushi Komori (Rikkyo Univ.). Moreover, based on Matsumoto's previous work, we obtained a functional equation of the double zeta-function which can be regarded as a double analogue of that of Riemann's zeta-function. In addition, he studied double Dirichlet series of Eisenstein type involving hyperbolic functions, and gave some formulas for them at positive integers.
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Report
(3 results)
Research Products
(44 results)
