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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机译:设 F 为第一类的全实数域,设 K 为以 F 为最大实数子域的 CM 域。对于每个正整数 N,我们在 F 上构造一个具有某些二元二次形式的类群,该类群与 K 模 N 的射线类群同构,进一步假设 F 的窄类数为 1,我们根据希尔伯特模函数的奇异值构造 K 反射场的类域.
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