Singular values of some modular functions and their applications to class fields

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Since the modular curve X(5) = Gamma(5)\h* has genus zero, we have a field isomorphism K(X(5)) approximate to C(X(2)(z)) where X(2)(z) is a product of Klein forms. We apply it to construct explicit class fields over an imaginary quadratic field K from the modular function j(Delta,25)(z) := X(2)(5z). And, for every integer N >= 7 we further generate ray class fields K((N)) over K with modulus N just from the two generators X(2)(z) and X(3)(z) of the function field K(X(1)(N)), which are also the product of Klein forms without using torsion points of elliptic curves.
Publisher
SPRINGER
Issue Date
2008-08
Language
English
Article Type
Article
Citation

RAMANUJAN JOURNAL, v.16, no.3, pp.321 - 337

ISSN
1382-4090
DOI
10.1007/s11139-007-9093-x
URI
http://hdl.handle.net/10203/87594
Appears in Collection
MA-Journal Papers(저널논문)
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