On Ramanujan's cubic continued fraction as a modular function
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概要
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We first extend the results of Chan ([4]) and Baruah ([2]) on the modular equations of Ramanujan's cubic continued fraction $C(\tau)$ to all primes $p$ by finding the affine models of modular curves and then derive Kronecker's congruence relations for these modular equations. We further show that by its singular values we can generate ray class fields modulo 6 over imaginary quadratic fields and find their class polynomials after proving that $1/C(\tau)$ is an algebraic integer.
著者
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Koo Ja
Department Of Mathematical Sciences Korea Advanced Institute Of Science And Technology
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Park Yoon
Department Of Mathematics Pohang University Of Science And Technology
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Park Yoon
Department Of Dermatology And Division Of Brain Korea 21 Project For Biomedical Science Korea Univer
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Koo Ja
Department Of Mathematical Sciences Kaist
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Cho Bumkyu
Department of Mathematics, Pohang University of Science and Technology
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Cho Bumkyu
Department Of Mathematics Pohang University Of Science And Technology
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Park Yoon
Department Of Bio And Chemical Engineering Hongik University
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Koo Ja
Department of Information Display, Hongik University, Seoul 121-791, Korea
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