Improving the trivial bound for $\ell$-torsion in class groups

Robert J. Lemke Oliver, Asif Zaman

For any number field $K$ with $D_K=|\mathrm{Disc}(K)|$ and any integer $\ell \ge 2$, we improve over the commonly cited trivial bound $|\mathrm{Cl}_K[\ell]| \leq |\mathrm{Cl}_K| \…