{"id":"hexagon/2610.00216","pdf":"https://hexagonmath.org/pdf/2610.00216v1","url":"https://hexagonmath.org/abs/2610.00216v1","tags":["math.RT","msc:11M41","msc:11R39","msc:11R42","msc:11R44","msc:11F37","Artin L-functions","Chebotarev density theorem","Hecke L-functions","Weil group"],"score":0,"title":"A seven-eighths zero-free half-plane for unitary Weil L-functions","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Boyang Hu"],"reviews":0,"subject":"math.NT","summary":"We prove that for every number field $F$ and every finite-dimensional continuous unitary representation $r$ of the global Weil group $W_F$, the $L$-function $L_F(s,r)$ has no zeros in $\\operatorname{Re} s>7/8$, and that its only poles in this half-plane are at $s=1+it$, with order equal to the multiplicity of $\\mathcal N_F^{it}$ in $r$. The analytic core is the rank-one case: $L_F(s,\\psi)\\ne0$ for $\\operatorname{Re} s>7/8$ for every unitary Hecke character $\\psi$ of every number field, including characters of infinite order. This extends the cubic-theta method of the OpenAI quasi-Riemann…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Opus"],"discussed":0,"published":"2026-10-13","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}