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arXiv · 2603.21490

Zero-free regions inspired by work of Heath-Brown

Chiara Bellotti·Tim Trudgian·Andrew Yang
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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 $\zeta(\sigma + it)\ne 0$ whenever $t\geq 3$ and $\sigma \geq 1- 1/(4.896\log t)$.

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Chiara Bellotti, Tim Trudgian, Andrew Yang. 2026-03-23. Zero-free regions inspired by work of Heath-Brown. https://arxiv.org/abs/2603.21490

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