ON RAMANUJANS CUBIC CONTINUED FRACTION AS A MODULAR FUNCTION

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We first extend the results of Chan ([4]) and Baruah (121) 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.
Publisher
TOHOKU UNIVERSITY
Issue Date
2010-12
Language
English
Article Type
Article
Keywords

SINGULAR-VALUES; FIELDS; EQUATIONS

Citation

TOHOKU MATHEMATICAL JOURNAL, v.62, no.4, pp.579 - 603

ISSN
0040-8735
DOI
10.2748/tmj/1294170348
URI
http://hdl.handle.net/10203/98887
Appears in Collection
MA-Journal Papers(저널논문)
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