ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS I

Title & Authors
ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS I
Yi, Jinhee; Cho, Man Gi; Kim, Jeong Hwan; Lee, Seong Hoi; Yu, Jae Myung; Paek, Dae Hyun;

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 $\small{{\varphi}}$ and $\small{{\psi}}$ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function $\small{{\psi}}$.
Keywords
theta functions;modular equations;
Language
English
Cited by
1.
ON EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY A MODULAR EQUATION OF DEGREE 9,;;

한국수학교육학회지시리즈B:순수및응용수학, 2016. vol.23. 3, pp.223-236
2.
ON SOME MODULAR EQUATIONS OF DEGREE 5 AND THEIR APPLICATIONS,;;

대한수학회보, 2013. vol.50. 4, pp.1315-1328
3.
ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS II,;;

대한수학회보, 2013. vol.50. 4, pp.1221-1233
1.
ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS II, Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1221
2.
ON SOME MODULAR EQUATIONS OF DEGREE 5 AND THEIR APPLICATIONS, Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1315
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