Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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AN AFFINE MODEL OF X0(mn)

  • Choi, So-Young (SCHOOL OF MATHEMATICS KOREA INSTITUTE FOR ADVANCED STUDY(KIAS)) ;
  • Koo, Ja-Kyung (DEPARTMENT OF MATHEMATICS KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY)
  • Published : 2007.05.31
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Abstract

We show that the modular equation ${\phi}^{T_n}_m$ (X, Y) for the Thompson series $T_n$ corresponding to ${\Gamma}_0$(n) gives an affine model of the modular curve $X_0$(mn) which has better properties than the one derived from the modular j invariant. Here, m and n are relative prime. As an application, we construct a ring class field over an imaginary quadratic field K by singular values of $T_n(z)\;and\;T_n$(mz).

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References

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Cited by

  1. AN AFFINE MODEL OF X0(pq)+q vol.26, pp.3, 2013, https://doi.org/10.14403/jcms.2013.26.3.641