Research toward to construct a concrete theory of Abelian functions

阿贝尔函数具体理论的构建研究

• 批准号: 19540002
• 负责人: ONISHI Yoshihiro
• 金额: $ 2.16万
• 依托单位: Iwate University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540002/
• 关键词: 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

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.

目前，我们不可能讨论没有三角函数的世界。阿贝尔函数是高度泛化三角函数的高级函数，在未来无疑将是非常重要的函数。任何阿贝尔函数都有一个称为“属”的数。三角函数属0，椭圆函数属1。虽然这些函数具有非常具体的理论，但属大于1的阿贝尔函数在具体理论方面却很差。通过这个项目，我构建了一个非常具体的理论的阿贝尔函数的属大于1。

项目成果

Determinant expressions in abelian functions for purely pentagonal curves of degree six

六次纯五边形曲线阿贝尔函数的行列式

• 发表时间: 2007
• 作者: S. Matsutani;Y. Onishi
• 通讯作者: Y. Onishi

Abelian functions for trigonal curves of degree four and determinantal formula in purely trigonal case

四次三角曲线的阿贝尔函数及纯三角情况下的行列式

• 发表时间: 2008
• 期刊: International Journal of Math. (印刷中)(掲載確定)
• 作者: J. C. Eibeck;V. Z. Enolski S. Matsutani;Y. Onishi;E. previato;Y. Onishi
• 通讯作者: Y. Onishi

Two topics concrete theory of Abelion functions

两题Abelion函数的具体理论

• 发表时间: 2008
• 作者: J.C. Eilbeck;V.Z. Enol'skii;S. Matustani,Y. Onishi;E. Previato;大西良博
• 通讯作者: 大西良博

Universal elliptic functions

通用椭圆函数

• 发表时间: 2010
• 期刊: arXiv.org http://arxiv.org/abs/1003.2927
• 作者: Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Iziuu Mori;Izuru Mori;毛利出;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;Izuru Mori;毛利 出;Izuru Mori;Y. Onishi;Yoshihiro Onishi;Yoshihiro Onishi
• 通讯作者: Yoshihiro Onishi

The addition law attached to a stratification for a hyperelliptic jacobian variety

超椭圆雅可比簇的分层附加定律

• 发表时间: 2008
• 期刊: Tokyo Journal of mathematics 31
• 作者: V.Z. Enolskii;S. Matsutani;Y. Onishi
• 通讯作者: Y. Onishi