Generation of class fields by using the Weber function

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Let K be an imaginary quadratic field and O-K be its ring of integers. Let h(E) be the Weber function on a certain elliptic curve E with complex multiplication by O-K. We show that if N (> 1) is an integer prime to 6, then the function h(E) alone generates the ray class field modulo NOK over K when evaluated at some N-torsion point of E, which would be a partial answer to the question mentioned in [10, p. 105]. (C) 2016 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2016-10
Language
English
Article Type
Article
Keywords

COMPLEX MULTIPLICATION

Citation

JOURNAL OF NUMBER THEORY, v.167, pp.74 - 87

ISSN
0022-314X
DOI
10.1016/j.jnt.2016.03.020
URI
http://hdl.handle.net/10203/209821
Appears in Collection
MA-Journal Papers(저널논문)
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