Normal bases of ray class fields over imaginary quadratic fields

Abstract

We develop a criterion for a normal basis (Theorem 2.4), and prove that the singular values of certain Siegel functions form normal bases of ray class fields over imaginary quadratic fields other than Q(root-1) and Q(root-3) (Theorem 4.2). This result would be an answer for the Lang-Schertz conjecture on a ray class field with modulus generated by an integer (>= 2) (Remark 4.3).