Ray class invariants over imaginary quadratic fields
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概要
- 論文の詳細を見る
Let $K$ be an imaginary quadratic field of discriminant less than or equal to -7 and $K_{(N)}$ be its ray class field modulo $N$ for an integer $N$ greater than 1. We prove that the singular values of certain Siegel functions generate $K_{(N)}$ over $K$ by extending the idea of our previous work. These generators are not only the simplest ones conjectured by Schertz, but also quite useful in the matter of computation of class polynomials. We indeed give an algorithm to find all conjugates of such generators by virtue of the works of Gee and Stevenhagen.
著者
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Shin Dong
Department Of Agricultural Chemistry The University Of Tokyo
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Jung Ho
Department Of Thoracic Surgery National Medical Center Seoul
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Koo Ja
Department Of Mathematical Sciences Kaist
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Jung Ho
Department Of Mathematical Sciences Kaist
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Shin Dong
Department Of Mathematical Sciences Natural Science Research Institute Kaist
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Jung Ho
Department of Electronics Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul 136-701, Korea
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Koo Ja
Department of Information Display, Hongik University, Seoul 121-791, Korea
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