Development of Number Theory based on Generic Polynomials

基于泛多项式的数论发展

• 批准号: 19540057
• 负责人: MIYAKE Katsuya
• 金额: $ 2.33万
• 依托单位: Waseda 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 2008
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540057/
• 关键词: 生成的多項式; 部分体問題; 2次体の類数問題; Cubic Thue equations; Hessian 曲線の捻り; 一般チルンハウス変換; 4次生成的多項式; 5次可解生成的多項式; Hessian曲線の捻り; 4次生成多項式; 5次可解生成多項式; 3次の数論

非アーベル的現象の探索法を探って, 一般次数対称群に対する生成的多項式の同型問題への方法を理論的に構築し, 「特殊化」によって活用する手法を確立した. さらに5次までの可解群に対する生成的多項式に対して同型問題を超えた共有体問題への解答を与えた. また3次の場合の数論への展開を進展させ, 古典的な2次体の類数問題への応用を深め, さらに8次巡回群に対する生成的多項式の有理数体上での「非存在」現象を解明した.

The exploration method of the phenomenon of non-symmetry is explored, the method of generating polynomial of general degree symmetry group is constructed theoretically, and the method of "specialization" is established. The solvable group of the fifth order is the polynomial generated by the congruence problem. In this paper, the development of number theory in the case of third-order is discussed, and the application of classical second-order class number problem is discussed. The non-existence phenomenon on the rational number field generated by the eight-order circuit group is explained.

项目成果

Two Expositions on Arithmetic of Cubics, The Proceedings of the Fourth China-Japan Seminar ed. By S

三次算术的两次论述，第四届中日研讨会论文集主编。

• 发表时间: 2007
• 期刊: Kanemitsu and J.-Y. Liu, World Scientific
• 作者: K.Hashimoto;A.Hoshi;and Y.Rikuna;Katsuya Miyake
• 通讯作者: Katsuya Miyake

Infinite family of imaginary cyclic fields of degree p-1with the p-rank of the ideal class groups of at least two

p-1 次假想循环场的无限族，其理想类群的 p 秩至少为 2

• 发表时间: 2007
• 期刊: Tsinghua Sci.Technol. 12,no.4
• 作者: Katsuya Miyake;Teiji Takagi;Akinari Hoshi and Katsuya Miyake;Toru Komatsu;Katsuya Miyake;Akinari Hoshi and Katsuya Miyake;Shinichi Katayama and Yasuhiro Kishi
• 通讯作者: Shinichi Katayama and Yasuhiro Kishi

ある2次体のイデアル類群について

关于某个二次域的理想类群

• 发表时间: 2008
• 作者: Katsuya Miyake;Teiji Takagi;Akinari Hoshi and Katsuya Miyake;Toru Komatsu;Katsuya Miyake;Akinari Hoshi and Katsuya Miyake;Shinichi Katayama and Yasuhiro Kishi;Akinari Hoshi and Katsuya Miyake;Akinari Hoshi and Katsuya Miyake;Akinari Hoshi and Katsuya Miyake;Toru Komatsu;Katsuya Miyake;Katsuya Miyake;A.Hoshi and Y.Rikuna;Toru Komatsu;Toru Komatsu;Toru Komatsu;Akinari Hoshi;Yasuhiro Kishi;Akinari Hoshi and Katsuya Miyake;Yasuhiro Kishi
• 通讯作者: Yasuhiro Kishi

Founder of the Japanese School of Modern Mathematics, Japan. Jour. of Math.

日本近代数学学派创始人。

• 发表时间: 2007
• 期刊: 3rd Series 2
• 作者: Katsuya Miyake;Teiji Takagi
• 通讯作者: Teiji Takagi

Tschirnhausen Transformation of a Cubic Generic Polynomial and a 2-dimensional Involutive Cremona Transformation

三次泛型多项式的 Tschirnhausen 变换和二维对合 Cremona 变换

• 发表时间: 2007
• 期刊: Proc.Japan Acad. 83,Ser.A
• 作者: Katsuya Miyake;Teiji Takagi;Akinari Hoshi and Katsuya Miyake;Toru Komatsu;Katsuya Miyake;Akinari Hoshi and Katsuya Miyake
• 通讯作者: Akinari Hoshi and Katsuya Miyake