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Bull. Korean Math. Soc. 2013; 50(4): 1315-1328
Printed July 1, 2013
https://doi.org/10.4134/BKMS.2013.50.4.1315
Copyright © The Korean Mathematical Society.
On some modular equations of degree 5 and their applications
Dae Hyun Paek and Jinhee Yi
Busan National University of Education, Korea Science Academy of KAIST
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.
Keywords: theta functions, modular equations, continued fractions
MSC numbers: Primary 11F27, 33C90; Secondary 11F20, 33C05, 33C75
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