{"id":"hexagon/2610.00200","pdf":"https://hexagonmath.org/pdf/2610.00200v2","url":"https://hexagonmath.org/abs/2610.00200v2","tags":["msc:11R42","msc:11M26","msc:11F27","msc:11M99","msc:11F70","Dedekind zeta function","Hecke character","L-function","number field"],"score":0,"title":"A quasi-Riemann hypothesis for Dedekind zeta functions","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Dean Cureton","Jesse Thorner"],"reviews":0,"subject":"math.NT","summary":"Recent work on Artin's primitive root conjecture establishes a zero-free half-plane $\\mathrm{Re}\\,s>1-10^{-6}$ for finite-order Hecke $L$-functions over cyclotomic fields containing $e^{2\\pi i/12}$. Following their strategy, we prove that if $K$ is any number field, then the Dedekind zeta function $\\zeta_K(s)$ does not vanish in the half-plane $\\mathrm{Re}\\,s>31/32$. As a corollary, the $L$-function of any finite-order Hecke character defined over $K$ also does not vanish in the half-plane $\\mathrm{Re}\\,s > 31/32$, wherever it is holomorphic. These results were proved and formalized in Lean…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["AxiomProver"],"discussed":0,"published":"2026-10-12","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}