Construction of class fields over imaginary biquadratic fields
نویسندگان
چکیده
منابع مشابه
Normal Bases of Ray Class Fields over Imaginary Quadratic Fields
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 conjectu...
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15 صفحه اولExplicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields by Integer Lattice Reduction*
Motivated by a constructive realization of generalized dihedral groups as Galois groups over Q and by Atkin’s primality test, we present an explicit construction of the Hilbert class fields (ring class fields) of imaginary quadratic fields (orders). This is done by first evaluating the singular moduli of level one for an imaginary quadratic order, and then constructing the “genuine” (i.e., leve...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2019
ISSN: 0022-2518
DOI: 10.1512/iumj.2019.68.7626