CLASS FIELDS FROM THE FUNDAMENTAL THOMPSON SERIES OF LEVEL N = o(g)

Title & Authors
CLASS FIELDS FROM THE FUNDAMENTAL THOMPSON SERIES OF LEVEL N = o(g)
CHOI So YOUNG; Koo JA KYUNG;

Abstract
Thompson series is a Hauptmodul for a genus zero group which lies between $\small{\Gamma}$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 $\small{T_g}$($\small{\alpha}$) (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 ($\small{{\zeta}N + {\zeta}_N^{-1}}$), and over a field K ($\small{{\zeta}N}$). Furthermore, we find an explicit formula for the conjugates of Tg ($\small{\alpha}$) to calculate its minimal polynomial where $\small{\alpha}$ ($\small{{\in}{\eta}}$) is the quotient of a basis of an integral ideal in K.
Keywords
modular functions;Thompson series;class fields;
Language
English
Cited by
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