TITLE: On Zeta function zeros in the critical strip
QUESTION [6 upvotes]: I have been reading about Riemann Zeta function and have been thinking about it for some time.
Has anything been published regarding upper bound for the real part of zeta function zeros as the imaginary part of the zeros tend to infinity?
Thanks

REPLY [3 votes]: De La Vallee-Pousin's theorem has been improved by Korobov and Vinogradov in the 50's and I believe their result is the strongest known asymptotic zero free region, cf. The Riemann zeta-function: Theory and applications by Alexandar Ivic. One can find more recent papers but my impression is that they don't touch the main exponents and so relatively tractable problems seem to be improving the constants, or giving explicit bounds on the constants etc.