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CLASS FIELDS FROM THE FUNDAMENTAL THOMPSON SERIES OF LEVEL N
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 Title & Authors
CLASS FIELDS FROM THE FUNDAMENTAL THOMPSON SERIES OF LEVEL N
CHOI So YOUNG; Koo JA KYUNG;
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 Abstract
Thompson series is a Hauptmodul for a genus zero group which lies between o(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class fields over an imaginary quadratic field K from the Thompson series () (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 (), and over a field K (). Furthermore, we find an explicit formula for the conjugates of Tg () to calculate its minimal polynomial where () is the quotient of a basis of an integral ideal in K.
 Keywords
modular functions;Thompson series;class fields;
 Language
English
 Cited by
 References
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