Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function

We prove that the Riemann zeta-function ζ(σ+it)ζ(σ+it) has no zeros in the region σ≥1−1/(5.573412log⁡|t|)σ≥1−1/(5.573412log⁡|t|) for |t|≥2|t|≥2. This represents the largest known zero-free region within the critical strip for 3.06⋅1010<|t|