Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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MODULAR POLYNOMIALS FOR MODULAR CURVES X0+(N)

  • Choi, SoYoung (Department of Mathematics Education Dongguk University)
  • Received : 2011.06.01
  • Accepted : 2011.08.25
  • Published : 2011.09.30
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Abstract

We show that for all $N{\geq}1$, the modular function field $K(X_0^+(N))$ is generated by j(z)j(Nz) and j(z) + j(Nz) over ${\mathbb{C}}$, where j(z) is the modular invariant. Moreover we derive the defining equation of the the modular function field $K(X_0^+(N))$ from the classical modular polynomial ${\Phi}_N(X, Y )$.

Keywords

References

  1. S. Lang, Elliptic Functions, Springer-Verlag, 1987.
  2. G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan, No. 11, Tokyo Prineton, 1971.