Generation of ray class fields of imaginary quadratic fields

Let K be an imaginary quadratic field other than Q(sqrt(-1)) and Q(sqrt(-3)), and let O_k be its ring of integers. Let N be a positive integer such that N=5 or N≥7. In this paper, we generate the ray class field modulo NO_K over K by using a single x-coordinate of an elliptic curve with complex multiplication by O_K.

1. Introduction

2. Fields of modular functions

3. Theory of complex multiplication

4. Inequalities on special values of modular functions

5. Generation of ray class elds

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