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연구기관
수리과학연구소
Journal papers
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Composition law and complex multiplication
Title
Composition law and complex multiplication
Authors
Eum I.S.
;
Jung H.Y.
;
Koo J.K.
;
Shin D.H.
Ewha Authors
정호윤
SCOPUS Author ID
정호윤
Issue Date
2020
Journal Title
Journal of Number Theory
ISSN
0022-314X
Citation
Journal of Number Theory vol. 209, pp. 396 - 420
Keywords
Binary quadratic forms
;
Class field theory
;
Complex multiplication
;
Modular functions
Publisher
Academic Press Inc.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
Let K be an imaginary quadratic field of discriminant dK, and let n be a nontrivial integral ideal of K in which N is the smallest positive integer. Let QN(dK) be the set of primitive positive definite binary quadratic forms of discriminant dK whose leading coefficients are relatively prime to N. We adopt an equivalence relation ∼n on QN(dK) so that the set of equivalence classes QN(dK)/∼n can be regarded as a group isomorphic to the ray class group of K modulo n. We further establish an explicit isomorphism of QN(dK)/∼n onto Gal(Kn/K) in terms of Fricke invariants, where Kn denotes the ray class field of K modulo n. This would be a certain extension of the classical composition theory of binary quadratic forms, originated and developed by Gauss and Dirichlet. © 2019 Elsevier Inc.
DOI
10.1016/j.jnt.2019.09.005
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