Singular values of principal moduli

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Let g be a principal modulus with rational Fourier coefficients for a discrete subgroup of SL2(R) lying in between Gamma(N) and Gamma(0)(N)(dagger) for a positive integer N. Let K be an imaginary quadratic field. We introduce a relatively simple proof, without using Shimura's canonical model, of the fact that the singular value of g generates the ray class field modulo N or the ring class field of the order of conductor N over K. Further, we construct a primitive generator of the ray class field K-c of arbitrary modulus c over K from Hasse's two generators. (C) 2012 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2013-02
Language
English
Article Type
Article
Keywords

CLASS FIELDS

Citation

JOURNAL OF NUMBER THEORY, v.133, no.2, pp.475 - 483

ISSN
0022-314X
DOI
10.1016/j.jnt.2012.08.006
URI
http://hdl.handle.net/10203/103415
Appears in Collection
MA-Journal Papers(저널논문)
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