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.
Publié le : 2010-05-15
Classification:
Ramanujan cubic continued fraction,
modular form,
class field theory,
11Y65,
11F11,
11R37,
11R04,
14H55
@article{1294170348,
author = {Cho, Bumkyu and Koo, Ja Kyung and Park, Yoon Kyung},
title = {On Ramanujan's cubic continued fraction as a modular function},
journal = {Tohoku Math. J. (2)},
volume = {62},
number = {1},
year = {2010},
pages = { 579-603},
language = {en},
url = {http://dml.mathdoc.fr/item/1294170348}
}
Cho, Bumkyu; Koo, Ja Kyung; Park, Yoon Kyung. On Ramanujan's cubic continued fraction as a modular function. Tohoku Math. J. (2), Tome 62 (2010) no. 1, pp. 579-603. http://gdmltest.u-ga.fr/item/1294170348/