zeta function-the elegant dance of the convergence line

third trial, the convergence line should form a loop, it would be necessary, if Riemann hypothesis would be false, then we have two roots symmetrical to the critical line. But the two halfs are too different-(determined by the enlarging vectors and segments)-I suppose, there are not only no two roots, but no two values at all symmetrical to Re(s)=0.5 causing the functional values coinciding at the same point.- The cornu spirals consist of many vectors, each one extending to modulus 1, whereas in the first half we have single vectors-this makes the cornu spirals growing exponentially, the second half of the convergence line is so straight and rigid. This makes it difficult to tie a loop as needed, therefore the RH is at least plausible)(more details may be found in(german) neuk5.pdf downloadable at : http://thomasfractalkromer.de/
See wonderful "a geometric perspective on the Riemann zeta function´s partial sums" of Carl Erickson.
The zeta function is diverging, but the same considerations and RH as well hold for the Dirichlet eta function, the alternating zeta function, and this does converge absolutely.

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[TRAJEKTORULM]

@nicodougy thank you for your comment. The video sould show, that the movement of the point of convergence over the complex plane is extremely(or quite) different, regarding the half representing the values 1 > Re(s) > 0.5 than from 0.5 towards 0. (because the single vectors are all of length 1 at Re(s)=0, and there are so many vectors at each swung segment, each cornu spiral of the second half of the zeta function.(Both halfs are symmetric for Re(s)=0.5, therefore the zeroes result.Continued

[nicodougy]

Extremely nice video! I realize when I see this, that it is not just that all zero have always Re=1/2 but that every time Zeta(1/2+ai) goes next to zero, it always passes by zero and never misses it! It is like it is attracted by it! I never realized that before watching your video...

On the other hand I am not sure I understand what all the other stuffs around should represent, but that does not look important as long as I get the meaning of the line. Thanks anyways...