| Project/Area Number |
22540165
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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 |
Basic analysis
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| Research Institution | Kitami Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MANO Toshiyuki 琉球大学, 理学部, 准教授 (60378594)
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| Co-Investigator(Renkei-kenkyūsha) |
SUZUKI Norio 北見工業大学, 工学部, 准教授 (80211986)
YAMADA Hiroshi 北見工業大学, 工学部, 教授 (50210472)
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| Project Period (FY) |
2010-10-20 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | Wirtinger 積分 / テータ因子 / アーベル曲面 / ツイストコホモロジー / ツイストホモロジー / テータ函数 / 超幾何積分 / Dolbeaultコホモロジー / スペクトル系列 / シュレジンガー変換 / パデ近似 / Wirtinger積分 / 解析学 / 複素トーラス / 対数的ドラーム複体 / モノドロミー / ツイストホモロジー類 / ガルニエ系 / コホモロジー / 積分表示 / 楕円曲線 / パンルヴェ方程式 |
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| Research Abstract |
The Wirtinger integral is obtained by lifting the Euler integral of the hypergeometric function on an elliptic curve, and is written as an integral of complex power product of four theta functions. There are two directions for generalizing the Wirtinger integral. In one direction, an ordinary differential equation satisfied by the integral of the multiplicative function on an elliptic curve with branch points more than 4 is determined, and the relation between that integral and monodromy preserving deformation theory is studied. In the other direction, the structure of twisted (co)homology groups of an abelian surface minus theta divisors, which will be the space of generalized integrals, is studied.
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