Explicit bounds for the Riemann zeta function and a new zero-free region

We prove that |ζ(σ+it)|≤70.7|t|4.438(1−σ)3/2log2/3⁡|t| for 1/2≤σ≤1 and |t|≥3. As a consequence, we improve the explicit zero-free region for ζ(s), showing that ζ(σ+it) has no zeros in the region σ≥1−1/(53.989(log⁡|t|)2/3(log⁡log⁡|t|)1/3) for |t|≥3 and asymptotically in the region σ≥1−1/(48.0718(log⁡|t|)2/3(log⁡log⁡|t|)1/3) for |t| sufficiently large.