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A zero density estimate for Dedekind zeta functions
- Source :
- Int. Math. Res. Not. IMRN 2023, no. 8, 6739-6761
- Publication Year :
- 2019
-
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.<br />Comment: Considerably streamlined, small refinements to Theorems 1.1 and 1.2. 14 pages
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Int. Math. Res. Not. IMRN 2023, no. 8, 6739-6761
- Publication Type :
- Report
- Accession number :
- edsarx.1909.01338
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1093/imrn/rnac015