用韦伯函数生成以2、3、4或6为模的射线类场

Pub Date : 2018-01-01 DOI:10.4134/JKMS.J170220

H. Jung, J. Koo, D. Shin

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引用次数: 7

摘要

．设K是一个由整数O K组成的环的虚二次域。设E是一条椭圆曲线与O K的复数相乘，设E是E上的韦伯函数。设N∈{2,3,4,6}。我们证明了E在E上某个N -扭转点处单独求值会产生K模N O K的射线类场。这将是对Hasse和Ramachandra提出的问题的部分回答。

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Generation of ray class fields modulo 2, 3, 4 or 6 by using the Weber function

. Let K be an imaginary quadratic ﬁeld with ring of integers O K . Let E be an elliptic curve with complex multiplication by O K , and let h E be the Weber function on E . Let N ∈ { 2 , 3 , 4 , 6 } . We show that h E alone when evaluated at a certain N -torsion point on E generates the ray class ﬁeld of K modulo N O K . This would be a partial answer to the question raised by Hasse and Ramachandra.

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