Potential role of the elliptic modular j-function in the "Kronecker's dream of youth" for real quadratic fields
| Project/Area Number |
23654013
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
KANEKO Masanobu 九州大学, 数理(科)学研究科(研究院), 教授 (70202017)
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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 |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 楕円モジュラー関数 / 実二次体 / 類体 / マルコフ数 / 虚数乗法 / caliber / マルコフ二次無理数 / モジュラー形式 |
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| Research Abstract |
Although we have not yet succeeded in obtaining any arithmetic quantities from the "values" of the elliptic modular j-function, we have obtained on the way some arithmetic results concerning Markoff numbers. We have formulated a kind of Diophantine continuity of the values of j-function at Markoff irrationalities in terms of Farey parametrization of Markoff numbers.
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Report
(4 results)
Research Products
(26 results)
