Distribution of prime ideals of higher residue degree across ideal classes in the class groups

Prem Prakash Pandey

Published 2017-01-29Version 1

In this article we investigate the distribution of prime ideals of residue degree bigger than one across the ideal classes in the class group of a number field $L$. A criterion for the class group of $L$ being generated by the classes of prime ideals of residue degree $f>1$ is provided. Further, some consequences of this study on the solvability of norm equations for $L/\mathbb{Q}$ and on the problem of finding annihilators for relative extensions are discussed.