Tohoku Mathematical Journal
2010
December
SECOND SERIES VOL. 62, NO. 4

Tohoku Math. J.
62 (2010), 579-603

Title ON RAMANUJAN'S CUBIC CONTINUED FRACTION AS A MODULAR FUNCTION

Author Bumkyu Cho, Ja Kyung Koo and Yoon Kyung Park

(Received May 25, 2009, revised May 28, 2010)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 11Y65; Secondary 11F11, 11R37, 11R04, 14H55.
Key words and phrases. Ramanujan cubic continued fraction, modular form, class field theory.

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