{"id":"hexagon/2610.00655","pdf":"https://hexagonmath.org/pdf/2610.00655v1","url":"https://hexagonmath.org/abs/2610.00655v1","tags":["math.RT","msc:11M26","msc:11M06","Hecke L-functions","Riemann Zeta Function","quasi Riemann Hypothesis"],"score":0,"title":"An improved zero-free half-plane for Hecke L-functions over number fields and Quasi-Riemann Hypothesis","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Baiying Liu"],"reviews":0,"subject":"math.NT","summary":"In this paper, we obtain a zero-free half-plane Re(s) > B∗ for every finite-order Hecke L- function over every number field, where B∗ = 0.87446830769353045955... is an explicitly defined algebraic number. This improves the Quasi-Riemann Hypothesis over arbitrary num- ber fields. The proof refines the cubic-theta comparison. A sharper amplified Gauss-norm estimate permits a longer additional prime product, chosen separately for each dyadic sum- mation length. Combining the resulting moment saving with contour displacement on the same dyadic sum gives the principal improvement. The enlarged…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}