A Zero Density Estimate for Dedekind Zeta Functions

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 strong form Artin’s conjecture. We use this remove hypothesis Artin conjecture from work Pierce, Turnage-Butterbaugh, and Wood average error in Chebotarev theorem $\ell $-torsion ideal class groups.