The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane $\Re s\gt 7/8$

Abstract — v1

We prove that all finite-order Hecke L-functions over $\mathbb Q(\sqrt{-3})$ and all Dirichlet L-functions are zero-free in the half-plane $\Re s\gt 7/8$, with the principal pole at s = 1 allowed. In particular, the Riemann zeta function is zero-free in this half-plane, proving the quasi-Riemann hypothesis.