On some multiple series which include the real analytic Eisenstein series
| Project/Area Number |
23540032
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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 | Nihon University |
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Principal Investigator |
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 |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
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| Keywords | 数論 / 解析的整数論 / アイゼンシュタイン級数 / 多重ゼータ関数 / Mellin -Barns積分変換 / Lipschitz公式 / 風洞壁干渉計算 / Mellin-Barnes変換公式 / Eisenstein級数 / 多重ゼータ / 漸近展開 |
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| Research Abstract |
Our main achievement of the present project is to establish a transformation formula of some Barnes' type double Eisenstein series. We obtained a asymptotic expansion and various explicit formulas of the specific value of these Eisenstein series. The double analog of the Lipschits formula via the Mellin-Barnes integral transformation is the key ingredient in our proof.
We also derived a transformation formula for a certain kind of Eisenstein series occurs in aerodynamic interference calculations, which provides extensive understanding of some double series in wind-tunnel wall corrections.
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Report
(4 results)
Research Products
(27 results)
