I have been reading about Riemann Zeta function $\zeta(s)$ and have been thinking about it for some time. I did some calculations, and reached a conclusion where $\Re(\rho) \le \log_2(3) - 1$ as $\Im(\rho) \to \infty$ where $\rho$'s are the roots of Riemann Zeta function in the critical strip. Anyways, I know its not the place to discuss claimed proofs and similar stuff, but just to give a background of where I am coming from. So straight to the question.

Is there any similar result regarding upper bound ($< 1$) for the real part of the zeros zeta function as their imaginary parts tend to infinity?

Thanks

`$\lim_{t \to \infty} f(t) =0$`

. A bound of the form you describe would be major progress. $\endgroup$ – David E Speyer Oct 5 '10 at 10:49