Zero-free regions inspired by work of Heath-Brown

Chiara Bellotti; Tim Trudgian; Andrew Yang

Zero-free regions inspired by work of Heath-Brown

Number Theory 2026-03-24 v1

Authors: Chiara Bellotti , Tim Trudgian , Andrew Yang

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 $\sigma \geq 1- 1/(4.896\log t)$ .

Keywords

Riemann zeta function zero-free region Heath-Brown Linnik's constant explicit bounds

Cite

@article{arxiv.2603.21490,
  title  = {Zero-free regions inspired by work of Heath-Brown},
  author = {Chiara Bellotti and Tim Trudgian and Andrew Yang},
  journal= {arXiv preprint arXiv:2603.21490},
  year   = {2026}
}

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26 pages

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