[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2013.50.4.847

CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS USING y-COORDINATES OF ELLIPTIC CURVES

Koo, Ja Kyung (Department of Mathematical Sciences, KAIST)
Shin, Dong Hwa (Department of Mathematics, Hankuk University of Foreign Studies)

Publication Information

Journal of the Korean Mathematical Society / v.50, no.4, 2013 , pp. 847-864 More about this Journal

Abstract

By a change of variables we obtain new $y$ -coordinates of elliptic curves. Utilizing these $y$ -coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the $y$ -coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

Keywords

class field theory; complex multiplication; elliptic and modular units; modular functions;

Citations & Related Records

Reference

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