On evaluations of the modular $j$--invariant by modular equations of degree 2
Bull. Korean Math. Soc. 2015 Vol. 52, No. 1, 263-273
https://doi.org/10.4134/BKMS.2015.52.1.263
Printed January 31, 2015
Dae Hyun Paek and Jinhee Yi
Busan National University of Education, Korea Science Academy of KAIST
Abstract : We derive modular equations of degree 2 to establish explicit relations for the parameterizations for the theta functions $\varphi$ and $\psi$. We then find specific values of the parameterizations to evaluate some new values of the modular $j$--invariant in terms of $J_n$.
Keywords : theta functions, modular equations, modular $j$--invariant
MSC numbers : Primary 11F27, 11R29, 33C90; Secondary 33C05, 33E05
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