Constructing ray class fields of a real quadratic field using elliptic curves
Volume 187 / 2019
Acta Arithmetica 187 (2019), 219-232
MSC: Primary 11G05; Secondary 11R37, 11Y40.
DOI: 10.4064/aa170425-14-5
Published online: 21 January 2019
Abstract
It is important to develop a method of explicitly constructing ray class fields of a real quadratic field. It is known that a conjectural Stark unit sometimes enables constructing such fields. On the other hand, there is an approach of Shimura relating such fields to abelian varieties. In this paper, we try to make some progress in this direction while giving examples of higher ray class fields.
