Bulletin of the Korean Mathematical Society (대한수학회보)

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

  • Paek, Dae Hyun (Department of Mathematics Education Busan National University of Education) ;
  • Yi, Jinhee (Department of Mathematics and Computer Science Korea Science Academy of KAIST)
  • Received : 2012.08.12
  • Published : 2013.07.31
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Abstract

We first derive some modular equations of degrees 3 and 9 and present their concise proofs based on algebraic computations. We then use these modular equations to establish explicit relations and formulas for the parameterizations for the theta functions ${\varphi}$ and ${\psi}$ In addition, we find specific values of the parameterizations to evaluate some numerical values of the cubic continued fraction.

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References

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  1. 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