Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS I

  • Yi, Jinhee (Department of Mathematics and Computer Science Korea Science Academy of KAIST) ;
  • Cho, Man Gi (Department of Mathematics and Computer Science Korea Science Academy of KAIST) ;
  • Kim, Jeong Hwan (Department of Mathematics and Computer Science Korea Science Academy of KAIST) ;
  • Lee, Seong Hoi (Department of Mathematics and Computer Science Korea Science Academy of KAIST) ;
  • Yu, Jae Myung (Department of Mathematics and Computer Science Korea Science Academy of KAIST) ;
  • Paek, Dae Hyun (Department of Mathematics Education Busan National University of Education)
  • Received : 2012.02.16
  • Published : 2013.05.31
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Abstract

We derive several modular equations and present their proofs based on concise algebraic computations. In addition, we establish explicit relations and formulas for some parameterizations for the theta functions ${\varphi}$ and ${\psi}$ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function ${\psi}$.

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References

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  1. ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS II vol.50, pp.4, 2013, https://doi.org/10.4134/BKMS.2013.50.4.1221
  2. ON SOME MODULAR EQUATIONS OF DEGREE 5 AND THEIR APPLICATIONS vol.50, pp.4, 2013, https://doi.org/10.4134/BKMS.2013.50.4.1315