Zero-free regions inspired by work of Heath-Brown

Abstract

We prove a new explicit zero-free region for the Riemann zeta-function, drawing substantially on Heath-Brown's seminal work on Linnik's constant. Using these ideas we are able to prove that $\hat{I}\P (\ddot{I}ƒ+it)\ne 0$ whenever $t\ge 3$ and $\ddot{I}ƒ\ge 1-1/(4.896\log t)$.

26 pages