Form class groups for extended ring class fields

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Let L be an extended ring class field of an imaginary quadratic field K other than and . We show that there is a form class group induced from a congruence subgroup which describes the Galois group of L over K in a concrete way. We also construct a primitive generator of L over K as a real algebraic integer which can be applied to certain quadratic Diophantine equations.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2019-04
Language
English
Article Type
Article
Citation

JOURNAL OF NUMBER THEORY, v.197, pp.13 - 36

ISSN
0022-314X
DOI
10.1016/j.jnt.2018.06.011
URI
http://hdl.handle.net/10203/248968
Appears in Collection
MA-Journal Papers(저널논문)
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