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Hi,

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

flag	asked Oct 5 2010 at 8:31 Roupam Ghosh 376●7

All results on zero-free regions have a strip with width tending to 0 as the imaginary part increases. – Charles Matthews Oct 5 2010 at 8:40

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All known results on zero free regions are of the form $\zeta(\sigma+it) \neq 0$ when $\sigma > 1 - f(t)$, for some function $f$ with $\lim_{t \to \infty} f(t) =0$ . A bound of the form you describe would be major progress. – David Speyer Oct 5 2010 at 10:49

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Honestly, you almostly certainly have an error. Your past questions have involved a number of elementary errors about analytic number theory and you are working on a problem which is notorious for drawing mathematicians into false proofs. In addition, if you are who I think you are, than 3 of your 6 papers on the arXiv have been withdrawn. (I am glad that you do withdraw errors!) Based on the little I know about you, you really need to find an advisor or mentor who can teach you how to do careful work in analytic number theory. – David Speyer Oct 5 2010 at 11:00

you may contact Prof.Bhaskar Bagchi of ISI,Bangalore.He was arguably the most interested person in India in RH.or you may contact me at bmat1013@isibang.ac.in. I am from ISI,Bangalore. – Koushik Feb 23 at 3:08

Prof.B.Bagchi spent 20 yrs trying to prove RH. – Koushik Feb 23 at 3:08

Fedor Petrov · Accepted Answer · 2010-10-05 09:22:28Z UTC

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There is no known non-trivial (less then 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.

answered Oct 5 2010 at 9:22

Fedor Petrov
6,789●1●12●38

	I was searching for papers having zero free regions... and most of them gave results like $\Re(\rho) > 1 - \beta$. Are you sure there are no such results? (I'll wait before accepting your answer) – Roupam Ghosh Oct 5 2010 at 9:36
	EDIT: by "no such results" I mean no results with $\Re(\rho) < c < 1$. Sorry for the typo – Roupam Ghosh Oct 5 2010 at 9:39
	I think after Speyer's comments I am ready to accept you answer... Thanks Fedor and Speyer !!! – Roupam Ghosh Oct 5 2010 at 11:20
	Here's my paper if anyone is actually interested :DDD docs.google.com/… – Roupam Ghosh Nov 11 2010 at 14:54

Tom Foregger · Answer 2 · 2011-03-15 19:16:28Z UTC

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If the proof is incorrect, what is the first equation in the paper that is incorrect?

answered Mar 15 2011 at 19:16

Tom Foregger
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You could look for yourself. I did, and the limit $\tau \to \infty$ at the beginning of Section 4 looks pretty dubious. – Emerton Mar 15 2011 at 19:31

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(5) is correct, hence (6) is wrong. – GH Mar 15 2011 at 20:56

Upper bound for real part of Riemann Zeta function zeros

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