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

## TL;DR

This paper studies how prime ideals with higher residue degrees distribute among ideal classes in number fields, providing criteria for generation of class groups and implications for norm equations and annihilators.

## Contribution

It introduces a criterion for the class group to be generated by prime ideals of higher residue degree and explores its implications.

## Key findings

- Criterion for class group generation by prime ideals of residue degree f>1
- Implications for solvability of norm equations in number fields
- Results on finding annihilators for relative extensions

## Abstract

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.