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



Upper bound for real part of Riemann Zeta function zeros
There is no known non-trivial (less than 1) bound for real parts of Zeta zeros (I guess, it is even called "weak Riemann conjecture" to find such a bound). So, your result is very-very interesting, maybe the most interesting result in mathematics for many years. 


