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.
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机译：假设$ K $是小于或等于$ -7 $的判别式的虚数二次方，而$ K _ {（N）} $是其射线类字段的模数，对大于$ 1 $的整数$ N $取模。我们证明了某些Siegel函数的奇异值通过扩展我们先前工作的想法而产生$ K _ {（N）} $超过$ K $。这些生成器不仅是Schertz猜想的最简单的生成器，而且在类多项式的计算方面也非常有用。我们确实给出了一种算法，可以借助Gee和Stevenhagen的工作找到这些生成器的所有共轭。
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