On Hasse-Ramachandra's problem

Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon

Published 2016-08-24Version 1

Let $K$ be an imaginary quadratic field, and let $N$ be an integer greater than $1$. We show that a special value of the Weber function alone generates the ray class field modulo $N$ over the base field $K$, except for the eight cases $N=2,\,3,\,4,\,6,\,12,\,18,\,24,\,36$. This would be a partial answer to the question raised by Hasse and Ramachandra.