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arXiv · 1912.08128

Form class groups and class fields of CM-fields

Ho Yun Jung·Ja Kyung Koo·Dong Hwa Shin·Dong Sung Yoon
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Abstract

Let $F$ be a totally real number field of class number one, and let $K$ be a CM-field with $F$ as its maximal real subfield. For each positive integer $N$, we construct a class group of certain binary quadratic forms over $F$ which is isomorphic to the ray class group of $K$ modulo $N$. Assuming further that the narrow class number of $F$ is one, we construct a class field of the reflex field of $K$ in terms of the singular values of Hilbert modular functions.

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Ho Yun Jung, Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon. 2019-12-17. Form class groups and class fields of CM-fields. https://arxiv.org/abs/1912.08128

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