충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제26권3호
  • /
  • Pages.641-645
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  • 2013
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  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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AN AFFINE MODEL OF X0(pq)+q

  • Choi, SoYoung (Department of Mathematics Education Dongguk University-Gyeongju)
  • 투고 : 2013.07.01
  • 심사 : 2013.07.24
  • 발행 : 2013.08.15
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초록

In this article, we show that the modular equation ${\Phi}_p^{T_q}(X,Y)$ of Thompson series $T_q$ corresponding to ${\Gamma}_0(q)+q$ gives an affine model of a modular curve $X_0(pq)+q$.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea(NRF)

참고문헌

  1. I. Chen and N. Yui, Singular values of Thompson series; Groups, Difference sets and Monster, de Gruyter, 255-326, 1995.
  2. S. Choi and J. Koo, An affine model of $X_0(mn)$, Bull. Korean Math. Soc. 44 (2007), no. 2, 379-383. https://doi.org/10.4134/BKMS.2007.44.2.379
  3. K. Mahler, On a class of non-linear functional equations connected with modular functions, J. Austral. Math. Soc. Ser. A 22 (1976), no. 1, 65-118. https://doi.org/10.1017/S1446788700013367
  4. T. Miyake, Modular Forms, Springer Verlag, 1989.
  5. G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan, no. 11, Tokyo Prineton, 1971.