Generation of ray class fields modulo 2, 3, 4 or 6 by using the Weber function

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Let K be an imaginary quadratic field with ring of integers O-K. Let E be an elliptic curve with complex multiplication by O-K, and let h(E) be the Weber function on E. Let N is an element of {2, 3, 4, 6}. We show that h(E) alone when evaluated at a certain N-torsion point on E generates the ray class field of K modulo NOK. This would be a partial answer to the question raised by Hasse and Ramachandra.
Publisher
KOREAN MATHEMATICAL SOC
Issue Date
2018-05
Language
English
Article Type
Article
Keywords

COMPLEX MULTIPLICATION; CURVES

Citation

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.55, no.2, pp.343 - 372

ISSN
0304-9914
DOI
10.4134/JKMS.j170220
URI
http://hdl.handle.net/10203/242427
Appears in Collection
MA-Journal Papers(저널논문)
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