Generation of class fields by using the Weber function.

Let K be an imaginary quadratic field and O K be its ring of integers. Let h E be the Weber function on a certain elliptic curve E with complex multiplication by O K . We show that if N (>1) is an integer prime to 6, then the function h E alone generates the ray class field modulo N O K over K when evaluated at some N -torsion point of E , which would be a partial answer to the question mentioned in [10, p. 105] . [ABSTRACT FROM AUTHOR]