Generation of class fields by using the Weber function
Number Theory
2014-10-14 v3
Abstract
Let be an imaginary quadratic field and be its ring of integers. Let be the Weber function on certain elliptic curve with complex multiplication by . We show that if () is an integer prime to , then the function alone generates the ray class field modulo over when evaluated at some -torsion point of .
Cite
@article{arxiv.1408.5650,
title = {Generation of class fields by using the Weber function},
author = {Ja Kyung Koo and Dong Hwa Shin and Dong Sung Yoon},
journal= {arXiv preprint arXiv:1408.5650},
year = {2014}
}