A short remark on the $\ell$-torsion part of class groups
Number Theory
2026-03-10 v1
Abstract
In a 2008 paper Ellenberg suggested a strategy to improve the known upper bounds for the -torsion part of class groups of number fields of fixed degree . Motivated by this he proposed a question about the number of primitive elements of small height in a number field. Here we answer Ellenberg's question. We also improve Heath-Brown's bound for the -torsion part of class groups of purely cubic number fields, and we generalize our improvement to pure fields of arbitrary odd degree .
Cite
@article{arxiv.2603.08121,
title = {A short remark on the $\ell$-torsion part of class groups},
author = {Martin Widmer},
journal= {arXiv preprint arXiv:2603.08121},
year = {2026}
}