{"id":"hexagon/2611.00082","pdf":"https://hexagonmath.org/pdf/2611.00082v1","url":"https://hexagonmath.org/abs/2611.00082v1","tags":["math.RT","msc:11M26","msc:11M06","Hecke L-function","Riemann Zeta Function","quasi Riemann Hypothesis"],"score":0,"title":"Selected character moments, zero-free half-planes 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 $\\Rea s>B_2$ for every finite-order Hecke $L$-function over every number field, where \\[ B_2=\\frac{777-\\sqrt{1081}}{852} =0.873381966613207519929\\ldots. \\] We adapt selected character-sum estimates and finite moment inductions to ideal-character sums over arbitrary number fields and restore ordinary sixth powers. Two finite moment inductions give an ordinary product estimate with length condition $n_1+n_2+2z\\le M$ for sufficiently fine original prime factors. Applying this estimate to zero detection and the averaged numerator in the cubic-theta…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}