Explicit zero-free regions for the Riemann zeta-function.

We prove that the Riemann zeta-function ζ (σ + i t) has no zeros in the region σ ≥ 1 - 1 / (55.241 (log | t |) 2 / 3 (log log | t |) 1 / 3 ) for | t | ≥ 3 . In addition, we improve the constant in the classical zero-free region, showing that the zeta-function has no zeros in the region σ ≥ 1 - 1 / (5.558691 log | t |) for | t | ≥ 2 . We also provide new bounds that are useful for intermediate values of | t | . Combined, our results improve the largest known zero-free region within the critical strip for 3 · 10 12 ≤ | t | ≤ exp (64.1) and | t | ≥ exp (1000) . [ABSTRACT FROM AUTHOR]