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 $\mathrm{Gal}(K/\mathbb{Q})\cong G$ 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.

Considerably streamlined, small refinements to Theorems 1.1 and 1.2. 14 pages

References in corpus (3)

• An unconditional $\mathrm{GL}(n)$ large sieve
• On an explicit zero-free region for the Dedekind zeta-function
• Improved lower bounds for the number of fields with alternating Galois group

Cited by in corpus (5)

• Distribution of Frobenius elements in families of Galois extensions
• An approximate form of Artin's holomorphy conjecture and non-vanishing of Artin $L$-functions
• $\ell$-torsion bounds for the class group of number fields with an $\ell$-group as Galois group
• Pointwise Bound for $\ell$-torsion in Class Groups II: Nilpotent Extensions
• Pointwise Bound for $\ell$-torsion in Class Groups: Elementary Abelian Extensions