Tohoku Mathematical Journal
2011
September
SECOND SERIES VOL. 63, NO. 3

Tohoku Math. J.
63 (2011), 413-426

Title RAY CLASS INVARIANTS OVER IMAGINARY QUADRATIC FIELDS

Author Ho Yun Jung, Ja Kyung Koo and Dong Hwa Shin

(Received August 17, 2010, revised January 27, 2011)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 11G16; Secondary 11F11, 11F20, 11G15, 11R37.
Key words and phrases. Elliptic units, class field theory, complex multiplication, modular forms.

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