nt.number theory – What are some consequences of zero free strip of the Riemann zeta function?

In a paper from arXiv yesterday https://arxiv.org/abs/2106.04644 the main result reads:

if $$zeta(s) = 0$$ then $$Re(s) leq 1 – 2h$$.

And $$h$$ is some constant $$> 0$$. If this result is indeed true, I’m sure there are many interesting consequences which was not possible to prove before. What are some of the consequences of results of this type? Thank you!