Tohoku Mathematical Journal

On Ramanujan's cubic continued fraction as a modular function

Bumkyu Cho, Ja Kyung Koo, and Yoon Kyung Park

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We first extend the results of Chan and Baruah 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.

Article information

Tohoku Math. J. (2), Volume 62, Number 4 (2010), 579-603.

First available in Project Euclid: 4 January 2011

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Zentralblatt MATH identifier

Primary: 11Y65: Continued fraction calculations
Secondary: 11F11: Holomorphic modular forms of integral weight 11R37: Class field theory 11R04: Algebraic numbers; rings of algebraic integers 14H55: Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]

Ramanujan cubic continued fraction modular form class field theory


Cho, Bumkyu; Koo, Ja Kyung; Park, Yoon Kyung. On Ramanujan's cubic continued fraction as a modular function. Tohoku Math. J. (2) 62 (2010), no. 4, 579--603. doi:10.2748/tmj/1294170348.

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