Normal Bases of Ray Class Fields over Imaginary Quadratic Fields
نویسندگان
چکیده
We first develop a criterion to determine normal bases (Theorem 2.4), and by making use of necessary lemmas which were refined from [3] we further prove that singular values of certain Siegel functions form normal bases of ray class fields over all imaginary quadratic fields other than Q( √−1) and Q( √−3) (Theorem 4.5 and Remark 4.6). This result would be an answer for the Lang-Schertz conjecture ([7] p. 292 or [13] p. 386) on a ray class field with any modulus generated by an integer ≥ 2 (Remark 4.7).
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