On the distribution of $\text{Cl}(K)[l^\infty]$ for degree $l$ cyclic fields

TL;DR

This paper proves that the distribution of $l^ ext{infty}$-class groups in cyclic degree $l$ fields aligns with Gerth's conjecture, leveraging recent advances by Alexander Smith under GRH.

Contribution

It establishes the distribution of $l^ ext{infty}$-class groups for cyclic degree $l$ fields, confirming a conjecture using new theoretical breakthroughs.

Findings

Distribution matches Gerth's conjecture under GRH

Utilizes recent breakthrough by Alexander Smith

Provides new insights into class group behavior

Abstract

Using a recent breakthrough of Alexander Smith, we prove that $l^\infty$-class groups of cyclic degree $l$ fields have the distribution conjectured by Gerth under GRH.