Algebraic and Analytic Research of Transcendental Numbers

超越数的代数与解析研究

• 批准号: 08640056
• 负责人: IITAKA Shigeru
• 金额: $ 1.28万
• 依托单位: Gakushuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640056/
• 关键词: Transcendental numbers; Algebraic independence; Diophantine equations; Functional equations

(a) In December 1996, "The 5-th Symposium of Transcendental Number Theory" was held at the main expense of this grant-in-aid. The fifteen research workers, including the three foreigners, delivered lectures on their new results concerning the transcendental number theory. For example,i) New applications of the theory of Mahler functions,ii) Exponential diophantine equations,iii) A new attempt on the theory of Nesterenko,iv) An extension of the theory of G-functions.The proceedings of this symposium was published.(b) We obtained new results on certain multiple series with "fractional powers" defined on an algebraic number field, which may be available for finding new transcendental numbers and deciding algebraic independence of special values. The multiple series is closely related to the zeta function on an algebraic number field with respect to Grossencharacter. By making use of this relation, we have proved the functional equation satisfied by the multiple series.

(a) 1996年12月，“第五届超越数论研讨会”以这项资助的主要费用举行。包括3名外国人在内的15名研究人员就他们关于超越数论的新成果发表了演讲。例如，i)马勒函数理论的新应用，ii)指数丢芬图方程，iii)涅斯捷连科理论的新尝试，iv) g函数理论的扩展。这次研讨会的论文集已经出版。(b)在代数数域上定义了若干“分数幂”多重级数，得到了新的结果，可用于寻找新的超越数和确定特殊值的代数独立性。复数级数与代数数域上的关于格罗森格律的zeta函数密切相关。利用这一关系，我们证明了多重级数所满足的泛函方程。

项目成果

A.Mizutani and T.Suzuki: "On the iterative and minimizing sequences for semilinear elliptic equations (II)" J.Indust. Appl. Math.13. 351-367 (1996)

A.Mizutani 和 T.Suzuki：“关于半线性椭圆方程的迭代和最小化序列 (II)”J.Indust。

藤原大輔: "The time slicing approximation of the fundamental solution for the Schrodinger equation with electromagnetic fields" J.Math.Soc.Japan. 49. 299-327 (1997)

Daisuke Fujiwara：“电磁场薛定谔方程基本解的时间切片近似”J.Math.Soc.Japan 49. 299-327 (1997)。

水谷明: "On the iterative and minimizing sequences for semilinear elliptic equations (II) (with T.Suzuki)" Japan J. Indust. Appl. Math.13. 351-367 (1996)

Akira Mizutani：“半线性椭圆方程的迭代和最小化序列（II）（与 T.Suzuki）”Japan J. Indust. 351-367（1996）。

T.Mitsui: "On certain multiple series with transformation formula in an algebraic number field" (preprint).

T.Mitsui：“关于代数数域中具有变换公式的某些多重级数”（预印本）。

S.T.Kuroda and H.Nagatani: "H_<-2> construction and Hamiltonians with intersection of various type." RIMS Kokyuroku. 994. 155-167 (1997)

S.T.Kuroda 和 H.Nagatani：“H_<-2> 构造和具有各种类型交集的哈密顿量。”