Normal bases of ray class fields over imaginary quadratic fields |
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Authors: | Ho Yun Jung Ja Kyung Koo Dong Hwa Shin |
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Institution: | 1. Department of Mathematical Sciences, KAIST, Daejeon, 373-1, Korea
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Abstract: | We develop a criterion for a normal basis (Theorem 2.4), and prove that the singular values of certain Siegel functions form normal bases of ray class fields over imaginary quadratic fields other than ${\mathbb{Q}(\sqrt{-1})}$ and ${\mathbb{Q}(\sqrt{-3})}$ (Theorem 4.2). This result would be an answer for the Lang-Schertz conjecture on a ray class field with modulus generated by an integer (≥2) (Remark 4.3). |
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