Tohoku Mathematical Journal

Ray class invariants over imaginary quadratic fields

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

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2), Volume 63, Number 3 (2011), 413-426.

Dates
First available in Project Euclid: 11 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1318338949

Digital Object Identifier
doi:10.2748/tmj/1318338949

Mathematical Reviews number (MathSciNet)
MR2851104

Zentralblatt MATH identifier
1279.11060

Subjects
Primary: 11G16: Elliptic and modular units [See also 11R27]
Secondary: 11F11: Holomorphic modular forms of integral weight 11F20: Dedekind eta function, Dedekind sums 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22] 11R37: Class field theory

Keywords
Elliptic units class field theory complex multiplication modular forms

Citation

Jung, Ho Yun; Koo, Ja Kyung; Shin, Dong Hwa. Ray class invariants over imaginary quadratic fields. Tohoku Math. J. (2) 63 (2011), no. 3, 413--426. doi:10.2748/tmj/1318338949. https://projecteuclid.org/euclid.tmj/1318338949


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References

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