| Project/Area Number |
18540172
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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 | Kyoto University |
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Principal Investigator |
HATA Masayoshi Kyoto University, 大学院・理学研究科, 准教授 (40156336)
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| Co-Investigator(Kenkyū-buntansha) |
上田 哲生 京都大学, 大学院理学研究科, 教授 (10127053)
永田 誠 京都大学, 数理解析研究所, 助手 (30293971)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,530,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | 数論 / PISOT数 / SALEM数 / 超越数 / 有理近似 / 小数部分 / PADE近似 / HERMITE積分 / 幾何数列 / Pisot数 / Salem数 / 無理数度 / MAHLER測度 / 素数定理 |
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| Research Abstract |
We successfully improved the earlier results on the lower bounds for the fractional part of e^n, where e is the base of natural logarithm and is known to be transcendental. This study was accomplished through that of Pisot and Salem numbers. Concerning the problem on Mahler measures (Lehmer problem) we can reduce it to an extremal problem of some non-linear functional.
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