Estimates For Integer Points on Algebraic Variety by using Diophantine Approxiwatic

使用丢番图近似估计代数簇上的整数点

• 批准号: 06640082
• 负责人: KOHNO Noriko
• 金额: $ 1.34万
• 依托单位: NIHON UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06640082/
• 关键词: Diophantine Approximation; Diophantine equation; Elliptic Curve; Algebraic curve; Integer point; Transcendence; Transcendental Number; Transcendence Measure; 周期; 擬周期; 零点評価; 代数多様体; 代数群; 対数一次形式; 超超数

For transcendental number x, we consider Diophantine approximations by algebraic number beta in terms of height of beta and degree of beta. By using such approximation, called transcendental (or transcendence) measure, we observe integer points on algebraic curves, for example, elliptic curves. We obtain here a refinement for such measure when x comes from coordinates of inverse image by exponential map of rational points of an algebraic group defined over a number field, which is defined as a non trivial extention of a simple abelian variety by the additine group. We get also some finiteness result concerning with integer solutions to certain exponential Diophantine equations.

对于超越数 x，我们根据代数数 beta 在 beta 的高度和 beta 的次数方面考虑丢番图近似。通过使用这种称为超越（或超越）测度的近似，我们观察代数曲线（例如椭圆曲线）上的整数点。当 x 来自于在数域上定义的代数群有理点的指数图的逆像坐标时，我们在这里获得了这种测度的改进，它被定义为由可加群定义的简单阿贝尔簇的非平凡扩展。我们还得到了一些关于某些指数丢番图方程的整数解的有限性结果。

项目成果

Noriko HIRATA-KOHNO, Tarlok Nath SHOREY: "On the Equation (x^m-1)/(x-1)=y^q with x power" Proceedings of Analytic Number Theory conference,Cambridge Press. (発表予定).

Noriko HIRATA-KOHNO，Tarlok Nath SHOREY：“On the Equation (x^m-1)/(x-1)=y^q with x power”，分析数论会议论文集，剑桥出版社（待出版）。

Ryuji SASAKI: "A remark on the moduli space of hyreielliptic period matrices with level 2 structure" Sonderdruck aus Arch. Math. 62. 83-87 (1994)

Ryuji SASAKI：“关于具有 2 级结构的 hyreelliptic 周期矩阵的模空间的评论”Sonderdruck aus Arch。

Susumu IROKAWA,Ryuji SASAKI: "On a family of quotieuts of Fermat curuei" Tsukuba J. Math. 19.No.1. (1995)121-139

Susumu IROKAWA，Ryuji SASAKI：“论 Fermat curuei 的一个家族” Tsukuba J. Math。

Susumu IROKAWA,Ryuji SASAKI: "On a family of quotieuts of Fermat curuei" Tsukuba J. Math. 19.No.1. (1995)

Susumu IROKAWA，Ryuji SASAKI：“论 Fermat curuei 的一个家族” Tsukuba J. Math。

Noriko HIRATA-KOHNO: "Diophantine Approximations on elliptic curves" RIMS Kokyoroku. (1996)

Noriko HIRATA-KOHNO：“椭圆曲线上的丢番图近似”RIMS Kokyoroku。