RAY CLASS INVARIANTS OVER IMAGINARY QUADRATIC FIELDS

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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.
Publisher
TOHOKU UNIVERSITY
Issue Date
2011-09
Language
English
Article Type
Article
Citation

TOHOKU MATHEMATICAL JOURNAL, v.63, no.3, pp.413 - 426

ISSN
0040-8735
URI
http://hdl.handle.net/10203/96045
Appears in Collection
MA-Journal Papers(저널논문)
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