English

Generation of class fields by using the Weber function

Number Theory 2014-10-14 v3

Abstract

Let KK be an imaginary quadratic field and OK\mathcal{O}_K be its ring of integers. Let hEh_E be the Weber function on certain elliptic curve EE with complex multiplication by OK\mathcal{O}_K. We show that if NN (>1>1) is an integer prime to 66, then the function hEh_E alone generates the ray class field modulo NOKN\mathcal{O}_K over KK when evaluated at some NN-torsion point of EE.

Keywords

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}
}
R2 v1 2026-06-22T05:38:12.033Z