| Project/Area Number |
19540002
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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 | Iwate University |
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Principal Investigator |
ONISHI Yoshihiro Iwate University, 人文社会科学部, 准教授 (60250643)
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| Co-Investigator(Kenkyū-buntansha) |
尾台 喜孝 岩手大学, 人文社会科学部, 准教授 (10204215)
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| Co-Investigator(Renkei-kenkyūsha) |
ODAI Yoshitaka 岩手大学, 人文社会科学部, 教授 (10204215)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 数論 / 数論幾何 / Abel函数 / 代数曲線 / Jacobi多様体 / Sigma函数 / Hurwitz整 / 楕円函数 / 代数学 / 幾何学 / アーベル函数 / 代数函数 / ベルヌーイ数 / Abelian functions / Jacobian varieties |
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| Research Abstract |
Currently, it is impossible for us to discuss the World without trgonometric functions. Abelian functions are advanced functions that highly generalizes the trigonomatric functions, and will be, no doubt, very important functions in the future. Any Abelian function has a number that called "genus". Trigonometric functions are of genus 0 and elliptic functions are of genus 1. Athough these functions have very concrete theory, Abelian functions of genus greater than 1 has so poor in concrete theory. Through this project I constructed a very concrete theory of Abelian functions of genus greater than 1.
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