GENERATORS AND DEFINING EQUATIONS OF MODULAR FUNCTION FIELDS
模函数场的生成器和定义方程
基本信息
- 批准号:12640036
- 负责人:
- 金额:$ 1.41万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2000
- 资助国家:日本
- 起止时间:2000 至 2002
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Our results are as follows.(1) We constracted new generators of the modular function field K(N)of the modular group Γ_1(N) by Weierstrass P-functuins and obatained a plain defining equation of the modular function field.(2) We gave some examples of the canonical power series solutions of the elliptic curve by constructing the generator of the genus 1 subfields of K(N) from the generators in (1) in the cases K(N) has genus 2.(3) We obatined an algorithm to determine the j-invariant of the elliptic curve corresponding to the solution of the defining equation. But this algorithm is *neffective for large N.In the course of studing the properties of the defining equation over the finite fields, the following two results were obtained.(4) We offered a method of constracting a family of elliptic curves over finite fields of cyclic rational point group of large order using the elliptic curve,rational over an algebraic number field, with complex multiplication.(5) We determined the trace of Frobenius endomoprphism of the elliptic curves with complex multipication R, where R is an order of discriminant divided by 3, 4,5 and its class number is 2 or 3.The results (4), (5) are applicable to the elliptic curve cryptosysytems.
我们的结果如下。(1)利用Weierstrass P-函数构造了模群Γ_1(N)的模函数域K(N)的新生成元,得到了模函数域K(N)的一个简单定义方程. (2)在K(N)亏格为2的情况下,通过由(1)中的生成元构造K(N)亏格为1的子域的生成元,给出了椭圆曲线的标准幂级数解的一些例子. (3)给出了一个确定椭圆曲线上与定义方程的解对应的j-不变量的算法。在研究有限域上定义方程的性质过程中,得到了以下两个结果。(4)利用代数数域上有理椭圆曲线的复数乘法,给出了大阶循环有理点群上有限域上椭圆曲线族的一种表示方法. (5)本文确定了具有复数乘法R的椭圆曲线的Frobenius自同态迹,其中R是被3,4,5整除的判别阶,其类数为2或3.结果(4),(5)适用于椭圆曲线密码系统.
项目成果
期刊论文数量(13)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
石田信彦, 石井伸郎: "Generators and defining equation of the modular function field of the group Γ1(N)"「Codes, Lattices, Modular forms and Vertex Operator Algebra」(山形大学)報告集. 78-85 (2001)
Nobuhiko Ishida、Nobuo Ishii:“群 Γ1(N) 模函数场的生成器和定义方程”“代码、格子、模形式和顶点算子代数”(山形大学)报告集 78-85 (2001)。
- DOI:
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- 影响因子:0
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- 通讯作者:
Nobuhiko Ishida, Noburo Ishii: "Generators and defining equation of the modular function field of the group Γ1(N)."Acta Arithmetica. 101.4. 303-320 (2002)
Nobuhiko Ishida、Noburo Ishii:“群 Γ1(N) 模函数场的生成元和定义方程”。《算术学报》101.4(2002)。
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- 影响因子:0
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- 通讯作者:
Noburo Ishii: "Families of cyclic groups of large order obtained from the elliptic curves with CM-8"DMIS Research Report. 01-1. 1-6 (2001)
Noburo Ishii:“用 CM-8 从椭圆曲线获得的大阶循环群族”DMIS 研究报告。
- DOI:
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- 影响因子:0
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Nobuhiko Ishida, Noburo Ishii: "Generators and defining equation of the modular function field of the group Γ1(N)"Proceeding on "Codes, Lattices, Modular forms and Vertex operator algebra" at Yamagata Univ. 78-85 (2001)
Nobuhiko Ishida、Noburo Ishii:“群 Γ1(N) 模函数场的生成器和定义方程”山形大学“代码、格、模形式和顶点算子代数”论文集 78-85 (2001)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Noburo Ishii: "Families of cyclic groups of large order obtained from the elliptic curves with CM-8."DMIS Research Report. 01-1. 1-6 (2001)
Noburo Ishii:“用 CM-8 从椭圆曲线获得的大阶循环群族。”DMIS 研究报告。
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ISHII Noburo其他文献
ISHII Noburo的其他文献
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{{ truncateString('ISHII Noburo', 18)}}的其他基金
Study on arithmetic properties of modular function fields and elliptic curves by constructive methods.
用构造方法研究模函数域和椭圆曲线的算术性质。
- 批准号:
15540042 - 财政年份:2003
- 资助金额:
$ 1.41万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Application of theory of elliptic curves to algebraic topology
椭圆曲线理论在代数拓扑中的应用
- 批准号:
02640071 - 财政年份:1990
- 资助金额:
$ 1.41万 - 项目类别:
Grant-in-Aid for General Scientific Research (C)
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