A Zero Density Estimate for Dedekind Zeta Functions

Abstract

Abstract Given a nontrivial finite group $G$, we prove the first zero density estimate for families of Dedekind zeta functions associated to Galois extensions $K/{\mathbb {Q}}$ with $\textrm {Gal}(K/{\mathbb {Q}})\cong G$ that does not rely on unproven progress towards the strong form of Artin’s conjecture. We use this to remove the hypothesis of the strong Artin conjecture from the work of Pierce, Turnage-Butterbaugh, and Wood on the average error in the Chebotarev density theorem and $\ell $-torsion in ideal class groups.