$\ell$-Torsion in Class Groups via Dirichlet $L$-functions

D. R. Heath-Brown

$\ell$-Torsion in Class Groups via Dirichlet $L$-functions

Number Theory 2025-01-07 v2

Authors: D. R. Heath-Brown

Abstract

For a prime $\ell$ , let $h_\ell(K)$ denote the $\ell$ -part of the class number of the number field $K$ . We investigate upper bounds for $h_\ell(K)$ when $K$ is quadratic or cubic, particularly in the case in which the discriminant of $K$ is smooth. This is achieved using properties of Dirichlet $L$ -functions.

Keywords

elliptic curves dirichlet characters l-functions

Cite

@article{arxiv.2412.07701,
  title  = {$\ell$-Torsion in Class Groups via Dirichlet $L$-functions},
  author = {D. R. Heath-Brown},
  journal= {arXiv preprint arXiv:2412.07701},
  year   = {2025}
}

Comments

Revised version with more references

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