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arXiv:2412.07701 [math.NT]AbstractReferencesReviewsResources

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

D. R. Heath-Brown

Published 2024-12-10, updated 2025-01-05Version 2

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.

Comments: Revised version with more references
Categories: math.NT
Subjects: 11R29, 11R16
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