A Zero Density Estimate for Dedekind Zeta Functions

Jesse Thorner, Asif Zaman

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)6739-6761
Number of pages23
JournalInternational Mathematics Research Notices
Volume2023
Issue number8
DOIs
StatePublished - Apr 1 2023

ASJC Scopus subject areas

  • General Mathematics

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