Nevanlinna theory from view point of discreteness
| Project/Area Number |
20740077
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo Institute of Technology (2011)
Kumamoto University (2008-2010) |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | ネバリンナ理論 / 値分布論 / タイヒミュラー空間 / 正則運動 / 高階導関数 / 正則曲線 / ネヴァンリンナ理論 / 有理型函数 / 整正則曲線 / 第二主要定理 / 高階微分 / Lang予想 / Goldberg予想 / 一般型多様体 / 有理型関数 / 双曲幾何学 / 分岐点 / 整関数 / 双曲幾何 / 基本群の非可換性 / 基本群 / 非可換 |
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| Research Abstract |
Between Nevanlinna theory on complex analysis and Diophantine geometry on Number theory, there are strong similarities, which are pointed out by several mathematician including Voijta. In this research, we studied Nevanlinna theory from the view point that there are discreteness principle in Nevanlinna theory, though the theory is based on the principle of continuous. In particular, I studied the proximity function in the theory from this view point, and proved the asymptotic equality in the second main theorem, then applied this to resolve Gol' dberg and Mues conjectures, which are classical conjectures in the theory of meromorphic functions.
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Report
(6 results)
Research Products
(17 results)
