ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS II

Title & Authors
ON SOME MODULAR EQUATIONS AND THEIR APPLICATIONS II
Paek, Dae Hyun; Yi, Jinhee;

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 $\small{{\varphi}}$ and $\small{{\psi}}$ In addition, we find specific values of the parameterizations to evaluate some numerical values of the cubic continued fraction.
Keywords
theta functions;modular equations;continued fractions;
Language
English
Cited by
1.
ON SOME MODULAR EQUATIONS OF DEGREE 5 AND THEIR APPLICATIONS,;;

대한수학회보, 2013. vol.50. 4, pp.1315-1328
1.
ON SOME MODULAR EQUATIONS OF DEGREE 5 AND THEIR APPLICATIONS, Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1315
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