Form class groups and class fields of CM-fields
Number Theory
2020-03-30 v2
Abstract
Let be a totally real number field of class number one, and let be a CM-field with as its maximal real subfield. For each positive integer , we construct a class group of certain binary quadratic forms over which is isomorphic to the ray class group of modulo . Assuming further that the narrow class number of is one, we construct a class field of the reflex field of in terms of the singular values of Hilbert modular functions.
Cite
@article{arxiv.1912.08128,
title = {Form class groups and class fields of CM-fields},
author = {Ho Yun Jung and Ja Kyung Koo and Dong Hwa Shin and Dong Sung Yoon},
journal= {arXiv preprint arXiv:1912.08128},
year = {2020}
}