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

Prem Prakash Pandey

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arXiv · 1701.08351

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

Prem Prakash Pandey

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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.

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Prem Prakash Pandey. 2017-01-29. Distribution of prime ideals of higher residue degree across ideal classes in the class groups. https://arxiv.org/abs/1701.08351

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