Class fields from the fundamental Thompson series of level N = o(g)

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Thompson series is a Hauptmodul for a genus zero group which lies between Gamma(0)(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class fields over an imaginary quadratic field K from the Thompson series T-g(alpha) (Theorem 4), which would be an extension of [3], Theorem 3.7.5 (2) by using the Shimura theory and the standard results of complex multiplication. Also we construct various class fields over K, over a CM-field K(zeta(N) + zeta(N)(-1)), and over a field K(zeta N). Furthermore, we find an explicit formula for the conjugates of T-g (alpha) to calculate its minimal polynomial where alpha(is an element of h) is the quotient of a basis of an integral ideal in K.
Publisher
KOREAN MATHEMATICAL SOCIETY
Issue Date
2005-03
Language
English
Article Type
Article
Citation

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.42, no.2, pp.203 - 222

ISSN
0304-9914
URI
http://hdl.handle.net/10203/91213
Appears in Collection
MA-Journal Papers(저널논문)
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