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arXiv · 1007.2312

Normal bases of ray class fields over imaginary quadratic fields

Ho Yung Jung·Ja Kyung Koo·Dong Hwa Shin
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Abstract

We develop a criterion for a normal basis, 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 $\mathbb{Q}(\sqrt{-3})$. This result would be an answer for the Lang-Schertz conjecture on a ray class field with modulus generated by an integer ($\geq2$).

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Ho Yung Jung, Ja Kyung Koo, Dong Hwa Shin. 2010-07-14. Normal bases of ray class fields over imaginary quadratic fields. https://arxiv.org/abs/1007.2312

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