| Project/Area Number |
18540006
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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 |
Algebra
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| Research Institution | Hirosaki University |
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Principal Investigator |
KOMATSU Takao Hirosaki University, 大学院・理工学研究科, 教授 (70300556)
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| Research Collaborator |
SHIOKAWA Iekata 慶応大学, 理工学部, 名誉教授
BOWMAN Dougalas 北イリノイ大学, 数理科学科, 教授(合衆国)
ELSNER Carsten ハノーヴァー応用科学大学, 教授(ドイツ)
LAOHAKOSOL Vichian カセットサート大学, 数学科, 教授(タイ)
CALDWELL Chris テネシー大学, マーチン校・数学統計学科, 教授(合衆国)
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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 |
¥3,660,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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 | 整数論 / 関数論 / 組合せ論 / 代数学 / Continued fractions / Tasoev continued fractions / Hurwitz continued fractions / Hyprgeometric functions / Diophantine Analysis / Leaping convergents / Hypergeometric functions |
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| Research Abstract |
Still new types of Hurwitz and Tasoev continued fractions, which belong to quasi-periodic continued fractions, have been found. Several typical relations between quasi-periodic continued fractions and hypergeometric functions, hyperbolic functions, Fibonacci-zeta functions have been discovered. Leaping convergents have been defined from the concept of convergents of quasi-periodic continued fractions. Characteristic properties of leaping convergents have been examined. Leaping convergents have been extensively defined on non-regular continued fractions and on general integer sequences.
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