2011 Fiscal Year Final Research Report
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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| 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 |
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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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