The clue to the proof of Riemann hypothesis

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Discussion Overview

The discussion revolves around a proposed clue to the proof of the Riemann hypothesis, specifically concerning the distribution of non-trivial zeros of the Riemann zeta function, ζ(s). The participants explore the implications of zeroes lying within the critical strip and the conditions under which they might be symmetrically distributed.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that if there are zeros with real parts between 0 and 1/2, then there must be an equal number of zeros symmetrically located around Re = 1/2.
  • It is proposed that the zeros would occur at Re(1/2 - x) and Re(1/2 + x) due to convergence conditions.
  • The participant argues that if two values of the Riemann zeta function at s1 = 1/2 - X + b*i and s2 = 1/2 + X + b*i are never equal, then the zeros cannot be symmetrically distributed around Re = 1/2.
  • Another participant expresses uncertainty about their contribution, acknowledging the possibility of being wrong while expressing a passion for mathematics.
  • There are revisions made to clarify the divergence criteria related to the distribution of zeros.

Areas of Agreement / Disagreement

Participants do not reach a consensus; multiple competing views and uncertainties about the proposed ideas remain evident throughout the discussion.

Contextual Notes

Some statements contain mixed terminology and unclear definitions, particularly regarding the divergence criteria and the conditions for zero distribution. The discussion does not resolve these ambiguities.

robert80
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This could be the way to proof. remember, this is not a proof.

today I found a clue to solution to Riemann hypothesis:

Let it be Riemann zeta function :ζ(s)

The proof that all the non trivial zeroes lie on the critical strip when s = 1/2 + it

let us suppose there are other zeroes having the real part between 0 < Re < 1/2

since to sattisfy the convergence of Re between 0 and 1/2 we know that THE VERY SAME AMOUNT OF ZEROS would accour symetrically to Re = 1/2

so the zeroes would accure on Re(1/2 - x) and they would occur on Re = (1/2 + x) because of convergence condition.

since the 2 values of Riemann Zeta functions of applying to it 2 different s1 and s2 s1 = 1/2 - X +b*i and s2 = 1/2 + X +b*i never equal, that means they couldn't have the same zeroes symetrically distributed to the Re = 1/2

---------------> the zeroes occur at Re=(1/2) if they exist.

The end.
 
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If this is of any help to somebody, I would be glad, if not I appologize. I will take now some days off of Math problems. And yes, there is a great possibility, I am wrong... But I feel really passionate about Math and I think I will go to study theoretical Math. Greetings to all.
 
Revised :

In order to sattisfy DIVERGENCE criteria on interval 1> Re > 0 the zeroes are distributed simetrically to the Re = 1/2. Sorry I mixed the terms ...
 
REVISED:This could be the way to proof. remember, this is not a proof.

today I found a clue to solution to Riemann hypothesis:

Let it be Riemann zeta function :ζ(s)

The proof that all the non trivial zeroes lie on the critical strip when s = 1/2 + it

let us suppose there are other zeroes having the real part between 0 < Re < 1/2

since to sattisfy the divergence criteria of Re between 0 and 1 we know that THE VERY SAME AMOUNT OF ZEROS would accour on the right of Re=1/2 symetrically to Re = 1/2

so the zeroes would accure on Re(1/2 - x) and they would occur on Re = (1/2 + x) because of divergence condition.

since the 2 values of Riemann Zeta functions of applying to it 2 different s1 and s2 s1 = 1/2 - X +b*i and s2 = 1/2 + X +b*i never equal, that means they couldn't have the same zeroes symetrically distributed to the Re = 1/2

---------------> the zeroes occur at Re=(1/2) if they exist.
 

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