Zero-free regions

Zero-free regions

Every non-trivial zero of the Riemann zeta function ζ(s) has real part 1/2. Equivalent forms involve the ξ-function, the explicit formula, and zero-density estimates on the critical strip.

Zero-free regions —lemma→ Riemann

There exists an effectively computable absolute c>0 such that ζ(σ+it)≠0 for σ ≥ 1 − c / (log(|t|+2))^{2/3}(log log(|t|+2 —lemma→ Zero-free regions

Zero-free regions —implies→ Critical line