Investigation of the behaviours of zeta and theta functions from a viewpoint of the theory of multiple hypergeometric functions
| Project/Area Number |
23540025
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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 | Keio University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
NODA Takumi 日本大学, 工学部, 准教授 (10350034)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 漸近展開 / ゼータ関数 / 多変数超幾何関数 |
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| Research Abstract |
The following items (1)---(3) describe the major consequences of our study during the fiscal years 2011--2013: (1) it is shown that complete asymptotic expansions exist for the double Shintani zeta-functions defined with $n$ complex variables $\mathbold{s}$ and $n$ complex parameters $\mathbold{z}$ when $\mathbold{z}$ becomes both small and large; (2) it is shown that complete asymptotic expansions exist for the double holomorphic Eisenstein series of two complex variables and with two complex parameters $z_j$ $(j=1,2)$ when the distance $|z_2-z_1|$ of the basis parameters becomes both small and large; (3) Let $q$ be a complex parameter with $|q|<1$. It is then shown that complete asymptotic expansions exist for certain weighted multiple $q$-integrals and $q$-differentials when $q\to1$.
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Report
(4 results)
Research Products
(30 results)
