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arXiv · 2412.07701

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

D. R. Heath-Brown
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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.

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D. R. Heath-Brown. 2024-12-10. $\ell$-Torsion in Class Groups via Dirichlet $L$-functions. https://arxiv.org/abs/2412.07701

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