CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS AND APPLICATIONS

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Let K be an imaginary quadratic field, H(O) the ring class field of an order O in K and K((N)) be the ray class field modulo N over K for a positive integer N. In this paper we provide certain general techniques of finding H(O) and K((N)) by using the theory of Shimura's canonical models via his reciprocity law, from which we partially extend some results of Schertz (Remark 4.2), Chen-Yui (Remark 4.2, Corollary 4.4), Cox-McKay-Stevenhagen (Corollary 4.5) and Cais-Conrad (Remark 5.3). And, we further reilluminate the classical result of Hasse by means of such a method (Corollary 5.4), and discover how to get one ray class invariant over K from Hasse's two generators (Corollary 5.5) which is different from Ramachandra's invariant [K. Ramachandra, Some applications of Kronecker's limit formulas, Ann. Math. 80 (1964), 104-148].
Publisher
OXFORD UNIV PRESS
Issue Date
2010-06
Language
English
Article Type
Article
Keywords

SINGULAR-VALUES; MODULI

Citation

QUARTERLY JOURNAL OF MATHEMATICS, v.61, no.2, pp.199 - 216

ISSN
0033-5606
DOI
10.1093/qmath/han035
URI
http://hdl.handle.net/10203/98999
Appears in Collection
MA-Journal Papers(저널논문)
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