Construction of ray class fields by smaller generators and applications

Ja Kyung Koo, Dong Sung Yoon

Published 2014-07-22, updated 2014-08-25Version 3

We first generate ray class fields over imaginary quadratic fields in terms of Siegel-Ramachandra invariants, which would be an extension of Schertz's result. And, by making use of quotients of Siegel-Ramachandra invariants we also construct ray class invariants over imaginary quadratic fields whose minimal polynomials have relatively small coefficients, from which we are able to solve certain quadratic Diophantine equations.