Riemann zeta function formula

I am using the eta function spirals to find a formula for all the center points of any spiral on the complex plane. This is based on my previous ideas about the center points of the zeta function.

(sorry in advance about my very poor english)

you can use s=a+bi when the real part is less then one and it will give you the same riemann zeta value that the functional equation will give you but without using reflection from zeta(1-s)

it came to my attention by a few people that there is a similar formula to this at mathworld - line 21

i am not sure if its the same formula i am showing in the video but only in a different variation

but if so then

it was conjectured by Knopp around 1930 and was proved by Hasse in 1930
plus i am not sure it was made in the same way i did it

i just wanted to add that my formula is more general case because i am using x in my formula
i dont know if he removed that x so that the formula will be nicer or he did it differently

but you can do nice things with that extra value :)

stuff i forgot to mention in the video:
=============================
(but in retrospect maybe i should have mention that)

1. the final formula is shorter so i put it in the thumbnail

2. i called "arm3" an arm and not a point because the summation starts from 1 to x+2 and this is a different arm from arm1. same goes for all the other arms!

3. the zeta formula holds for all complex s values except for s=1+i*2*(pi/ln2)*N where N is an integer.

but you can do a limit on both sides of s and you will see that
for any non zero integer of n you will get the same limit on both sides
and when N=0 then every side will give a different result meaning there is no limit at point zeta(1)

[nightmisterio]

I want to output primes on some programming language using these functions as a base, have you done that?

[wallstreetoneil]

Been spending some Covid time trying to understand the Riemann Hypothesis - I like what you've done here. I'm a Stats person that use to build a lot of models and this is something I would have done. It reminds me of one of my Actuarial Exams where you studied on techniques to accelerate finding zeroes. Well done. If you could, do you have an understanding of why, or if, the actual zero imaginary parts, the 14.xx and then higher, are actually important by themselves, or does the actual value have no information and it is just 'random', like the primes, and it is really only important the real part is 1/2? Many thanks

[kees-janhermans]

I really like your idea of any point being either the convergent endpoint, or the origin point of a spiral, and it makes the Zeta function very intuitive. Why is your generalization of the Zeta function not part of the wikipedia page, for example?

[michaelkoch]

If the proof can succeed, then this is the proof by contradiction, which leads to the desired result. As long as the assumption is still unproven, as long as the uniqueness is attainable. However, I suspect that this assumption has long since been proven and no one has noticed.