Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON SOME MODULAR EQUATIONS OF DEGREE 5 AND THEIR APPLICATIONS

  • 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 : 2012.09.27
  • Published : 2013.07.31
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Abstract

We first derive several modular equations of degree 5 and present their concise proofs based on algebraic computations. We then establish explicit relations and formulas for some parameterizations for the theta functions ${\varphi}$ and ${\psi}$ by using the derived modular equations. In addition, we find specific values of the parameterizations and evaluate some numerical values of the Rogers-Ramanujan continued fraction.

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References

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