Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CLASS FIELDS FROM THE FUNDAMENTAL THOMPSON SERIES OF LEVEL N = o(g)

  • CHOI So YOUNG (Korea Advanced Institute of Science and Technology Department of Mathematics) ;
  • Koo JA KYUNG (Korea Advanced Institute of Science and Technology Department of Mathematics)
  • Published : 2005.02.01
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Abstract

Thompson series is a Hauptmodul for a genus zero group which lies between $\Gamma$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 $T_g$($\alpha$) (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 Tg ($\alpha$) to calculate its minimal polynomial where $\alpha$ (${\in}{\eta}$) is the quotient of a basis of an integral ideal in K.

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References

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