Why doesn´t this proof the Riemann Hypothesis?

Why doesn´t this proof the Riemann Hypothesis?

Postby Guest » Sun May 17, 2020 1:18 pm

Im just curious... Why doesn´t this proof the Riemann Hypothesis? Where is it´s logical mistake:

When we assume - like Riemann did - that all the zeros are of the form c*i+[tex]\frac{1}{2}[/tex] we can say that this and only this has the property to give out zero when plugged into the Zeta Function.
We then can say that it must be true that c*i+[tex]\frac{1}{2}[/tex] \ne c*i+[tex]\frac{1}{r}[/tex] for every c \in R and for every c also every r \in R with r greater than 0, but smaller than 1 and r \ne 2.
This can easily be proofed by subtracting c*i from both sides like so:
c*i+[tex]\frac{1}{2}[/tex] \ne c*i+[tex]\frac{1}{r}[/tex] |-(c*i)
[tex]\frac{1}{2}[/tex] \ne [tex]\frac{1}{r}[/tex]
And this must be true, because as defined earlier r \ne 2
Guest
 

Re: Why doesn´t this proof the Riemann Hypothesis?

Postby Guest » Wed Jun 03, 2020 11:04 am

First, the verb is "prove", not "proof". "Proof", in this sense, is a noun.

Second you cannot (and Riemann did not) assume "that all the zeros are of the form c*i+
1/2". That is the hypothesis you are want to prove.

Yes, it is true that numbers of the form 1/2+ ci have that property. But that is not the "Rieman Hypothesis". The "Riemann Hypothesis" is that only numbers of that form have that property.
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